simp at voc_res_ss_Lcond
C : List TNode
L R : Finset Formula
ruleA : LocalRuleApp (L, R) C
ress : List SubPair
Lcond Rcond : Finset Formula
rule : LocalRule (Lcond, Rcond) ress
hC : C = applyLocalRule rule (L, R)
preproof : Lcond ⊆ L ∧ Rcond ⊆ R
c : TNode
cinC : c ∈ C
ℓ : Char
ℓ_in_c : (∃ a ∈ c.1, ℓ ∈ vocabOfFormula a) ∧ ∃ a ∈ c.2, ℓ ∈ vocabOfFormula a
Lφ : Formula
Lφ_in_cL : Lφ ∈ c.1
ℓ_in_Lφ : ℓ ∈ vocabOfFormula Lφ
not_Lφ_in_L : Lφ ∉ L
Lφ_in_res : ∃ res ∈ ress, Lφ ∈ res.1
res : SubPair
res_in_ress : res ∈ ress
Lφ_in_res_L : Lφ ∈ res.1
voc_res_ss_Lcond : voc res.1 ⊆ voc Lcond := localRule_does_not_increase_vocab_L rule res res_in_ress
⊢ ∃ ψ ∈ Lcond, ℓ ∈ voc ψ
C : List TNode
L R : Finset Formula
ruleA : LocalRuleApp (L, R) C
ress : List SubPair
Lcond Rcond : Finset Formula
rule : LocalRule (Lcond, Rcond) ress
hC : C = applyLocalRule rule (L, R)
preproof : Lcond ⊆ L ∧ Rcond ⊆ R
c : TNode
cinC : c ∈ C
ℓ : Char
ℓ_in_c : (∃ a ∈ c.1, ℓ ∈ vocabOfFormula a) ∧ ∃ a ∈ c.2, ℓ ∈ vocabOfFormula a
Lφ : Formula
Lφ_in_cL : Lφ ∈ c.1
ℓ_in_Lφ : ℓ ∈ vocabOfFormula Lφ
not_Lφ_in_L : Lφ ∉ L
Lφ_in_res : ∃ res ∈ ress, Lφ ∈ res.1
res : SubPair
res_in_ress : res ∈ ress
Lφ_in_res_L : Lφ ∈ res.1
voc_res_ss_Lcond : ∀ x ∈ res.1, vocabOfFormula x ⊆ Lcond.biUnion vocabOfFormula
⊢ ∃ ψ ∈ Lcond, ℓ ∈ voc ψ