url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
rw [Nat.add_assoc]
|
case mp.semiR
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ Nat.succ 0 < 1 + sizeOf l✝ + sizeOf r✝
|
case mp.semiR
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
apply Nat.lt_add_of_pos_right
|
case mp.semiR
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
first | (apply Nat.add_pos_left; apply sizeOf_pos)
| (apply Nat.add_pos_right; apply sizeOf_pos)
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
(apply Nat.add_pos_left; apply sizeOf_pos)
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
case mp.semiR.h.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
apply Nat.add_pos_left
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
case mp.semiR.h.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
apply sizeOf_pos
|
case mp.semiL.h.h
P✝ : Sort u_1
b : Bunch P✝
l✝ : BunchWithHole P✝
r✝ : Bunch P✝
h : (subst b l✝ ;ᵇ r✝) = b
⊢ 0 < sizeOf l✝
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
(apply Nat.add_pos_right; apply sizeOf_pos)
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
apply Nat.add_pos_right
|
case mp.semiR.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf l✝ + sizeOf r✝
|
case mp.semiR.h.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf r✝
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
apply sizeOf_pos
|
case mp.semiR.h.h
P✝ : Sort u_1
b l✝ : Bunch P✝
r✝ : BunchWithHole P✝
h : (l✝ ;ᵇ subst b r✝) = b
⊢ 0 < sizeOf r✝
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
rintro rfl
|
case mpr
P✝ : Sort u_1
b : Bunch P✝
Γ : BunchWithHole P✝
⊢ Γ = hole → subst b Γ = b
|
case mpr
P✝ : Sort u_1
b : Bunch P✝
⊢ subst b hole = b
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.subst_idem
|
[101, 9]
|
[116, 21]
|
simp
|
case mpr
P✝ : Sort u_1
b : Bunch P✝
⊢ subst b hole = b
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.idem_subst
|
[118, 9]
|
[120, 7]
|
rw [eq_comm]
|
P✝ : Sort u_1
b : Bunch P✝
Γ : BunchWithHole P✝
⊢ b = subst b Γ ↔ Γ = hole
|
P✝ : Sort u_1
b : Bunch P✝
Γ : BunchWithHole P✝
⊢ subst b Γ = b ↔ Γ = hole
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.idem_subst
|
[118, 9]
|
[120, 7]
|
simp
|
P✝ : Sort u_1
b : Bunch P✝
Γ : BunchWithHole P✝
⊢ subst b Γ = b ↔ Γ = hole
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.comp_hole
|
[148, 9]
|
[149, 30]
|
induction Γ <;> simp_all
|
P : Sort u_1
Γ : BunchWithHole P
⊢ Γ.comp hole = Γ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.comp_def
|
[151, 1]
|
[153, 55]
|
induction h1 <;> simp_all [comp, FunLike.coe, subst]
|
P : Sort u_1
h1 h2 : BunchWithHole P
b : Bunch P
⊢ ↑(h1.comp h2) b = ↑h1 (↑h2 b)
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_prop
|
[155, 9]
|
[157, 40]
|
cases Γ <;> simp [FunLike.coe, subst]
|
P : Sort u_1
b : Bunch P
φ : Typ P
Γ : BunchWithHole P
⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.prop_eq
|
[159, 9]
|
[162, 7]
|
rw [show (prop φ = _ ↔ _ = prop φ) from ⟨Eq.symm, Eq.symm⟩]
|
P : Sort u_1
φ : Typ P
b : Bunch P
Γ : BunchWithHole P
⊢ prop φ = ↑Γ b ↔ Γ = hole ∧ b = prop φ
|
P : Sort u_1
φ : Typ P
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.prop_eq
|
[159, 9]
|
[162, 7]
|
simp
|
P : Sort u_1
φ : Typ P
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_cunit
|
[164, 9]
|
[166, 40]
|
cases Γ <;> simp [FunLike.coe, subst]
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.cunit_eq
|
[168, 9]
|
[171, 7]
|
rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ cunit = ↑Γ b ↔ Γ = hole ∧ b = cunit
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.cunit_eq
|
[168, 9]
|
[171, 7]
|
simp
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_sunit
|
[173, 9]
|
[175, 40]
|
cases Γ <;> simp [FunLike.coe, subst]
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.sunit_eq
|
[177, 9]
|
[180, 7]
|
rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ sunit = ↑Γ b ↔ Γ = hole ∧ b = sunit
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.sunit_eq
|
[177, 9]
|
[180, 7]
|
simp
|
P : Sort u_1
b : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_comma
|
[182, 1]
|
[188, 20]
|
cases Γ <;> aesop
|
P : Sort u_1
b Δ₁ Δ₂ : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = (Δ₁ ,ᵇ Δ₂) ↔
Γ = hole ∧ b = (Δ₁ ,ᵇ Δ₂) ∨ (∃ Γ', Γ = commaL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = commaR Δ₁ Γ' ∧ ↑Γ' b = Δ₂
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_semi
|
[190, 1]
|
[196, 20]
|
cases Γ <;> aesop
|
P : Sort u_1
b Δ₁ Δ₂ : Bunch P
Γ : BunchWithHole P
⊢ ↑Γ b = (Δ₁ ;ᵇ Δ₂) ↔
Γ = hole ∧ b = (Δ₁ ;ᵇ Δ₂) ∨ (∃ Γ', Γ = semiL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = semiR Δ₁ Γ' ∧ ↑Γ' b = Δ₂
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
intro h
|
P : Sort u_1
Γ Γ' : BunchWithHole P
φ φ' : Bunch P
⊢ ↑Γ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
Γ Γ' : BunchWithHole P
φ φ' : Bunch P
h : ↑Γ φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
induction Γ generalizing Γ'
|
P : Sort u_1
Γ Γ' : BunchWithHole P
φ φ' : Bunch P
h : ↑Γ φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
case hole
P : Sort u_1
φ φ' : Bunch P
Γ' : BunchWithHole P
h : ↑hole φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case commaL
P : Sort u_1
φ φ' : Bunch P
l✝ : BunchWithHole P
r✝ : Bunch P
l_ih✝ :
∀ {Γ' : BunchWithHole P},
↑l✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑(commaL l✝ r✝) φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaL l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaL l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case commaR
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
r_ih✝ :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑(commaR l✝ r✝) φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case semiL
P : Sort u_1
φ φ' : Bunch P
l✝ : BunchWithHole P
r✝ : Bunch P
l_ih✝ :
∀ {Γ' : BunchWithHole P},
↑l✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑(semiL l✝ r✝) φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiL l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiL l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case semiR
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
r_ih✝ :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑(semiR l✝ r✝) φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
case hole => simp_all
|
P : Sort u_1
φ φ' : Bunch P
Γ' : BunchWithHole P
h : ↑hole φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp_all
|
P : Sort u_1
φ φ' : Bunch P
Γ' : BunchWithHole P
h : ↑hole φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑(semiR l✝ r✝) φ = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rw [eq_comm] at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ)
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
first | rw [eq_comma] at h | rw [eq_semi] at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ)
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h :
Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨
(∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rcases h with (⟨rfl,rfl⟩|⟨Γ'',rfl,h⟩|⟨Γ'',rfl,h⟩)
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h :
Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨
(∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
case inl.intro
P : Sort u_1
φ l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) →
(∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨
(∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case inr.inl.intro.intro
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = l✝
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
case inr.inr.intro.intro
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rw [eq_comma] at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑Γ' φ' = (l✝ ,ᵇ ↑r✝ φ)
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h :
Γ' = hole ∧ φ' = (l✝ ,ᵇ ↑r✝ φ) ∨
(∃ Γ'_1, Γ' = commaL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = commaR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rw [eq_semi] at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ)
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ' : BunchWithHole P
h :
Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨
(∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp
|
case inl.intro
P : Sort u_1
φ l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) →
(∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨
∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨
(∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rw [eq_comm] at h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = ↑r✝ φ
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑r✝ φ = ↑Γ'' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
rcases ih h with (h1|h2|⟨Δ,Δ',rfl,rfl,h3⟩)
<;> clear ih h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑r✝ φ = ↑Γ'' φ'
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
case inl
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ Γ'' : BunchWithHole P
h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ''
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
case inr.inl
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ Γ'' : BunchWithHole P
h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
case inr.inr.intro.intro.intro.intro
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨
(∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨
∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp [h1]
|
case inl
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ Γ'' : BunchWithHole P
h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ''
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp [h2]
|
case inr.inl
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ Γ'' : BunchWithHole P
h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝
⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨
∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
apply Or.inr
|
case inr.inr.intro.intro.intro.intro
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨
(∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨
∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨
∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
apply Or.inr
|
case inr.inr.intro.intro.intro.intro.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨
∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
iterate 2 (
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
)
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
intro ψ ψ'
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
ψ ψ' : Bunch P
⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp [h3]
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
ψ ψ' : Bunch P
⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
(
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
)
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => commaL _ _),rfl,?_⟩
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' r✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = commaL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' r✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑((fun x => commaL (Δ' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => commaR _ _),rfl,?_⟩
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = commaR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑((fun x => commaR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => semiL _ _),rfl,?_⟩
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' r✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = semiL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' r✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑((fun x => semiL (Δ' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => semiR _ _),rfl,?_⟩
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ
|
case inr.inr.intro.intro.intro.intro.h.h
P : Sort u_1
φ φ' l✝ : Bunch P
Δ Δ' : Bunch P → BunchWithHole P
h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
cases h
|
P : Sort u_1
φ φ' l✝ : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
h : ↑Γ'' φ' = l✝
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨
∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨
∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨
(∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨
∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
iterate 2 (
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
)
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
intro ψ ψ'
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
ψ ψ' : Bunch P
⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
simp
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
ψ ψ' : Bunch P
⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
(
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
)
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
first | refine ⟨(fun x => commaL _ _),rfl,?_⟩
| refine ⟨(fun x => commaR _ _),rfl,?_⟩
| refine ⟨(fun x => semiL _ _),rfl,?_⟩
| refine ⟨(fun x => semiR _ _),rfl,?_⟩
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => commaL _ _),rfl,?_⟩
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ Δ, Δ φ = commaL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => commaR _ _),rfl,?_⟩
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => commaR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => semiL _ _),rfl,?_⟩
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.eq_inv
|
[198, 1]
|
[239, 13]
|
refine ⟨(fun x => semiR _ _),rfl,?_⟩
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ
|
case refl
P : Sort u_1
φ φ' : Bunch P
r✝ : BunchWithHole P
ih :
∀ {Γ' : BunchWithHole P},
↑r✝ φ = ↑Γ' φ' →
(∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨
(∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ
Γ'' : BunchWithHole P
⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.idem
|
[241, 9]
|
[243, 21]
|
simp [FunLike.coe]
|
P : Sort u_1
Γ : BunchWithHole P
b : Bunch P
⊢ ↑Γ b = b ↔ Γ = hole
|
no goals
|
https://github.com/JamesGallicchio/brunched-invitations.git
|
3082c5ae68d2022b1439310f315a0038dae24e0c
|
BunchImpl/Bunch.lean
|
BunchImpl.BunchWithHole.idem'
|
[245, 9]
|
[247, 21]
|
simp [FunLike.coe]
|
P : Sort u_1
Γ : BunchWithHole P
b : Bunch P
⊢ b = ↑Γ b ↔ Γ = hole
|
no goals
|
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