induction a
case mk.mk
L : Language
inst✝³ : (k : ℕ) → DecidableEq (L.Func k)
inst✝² : (k : ℕ) → DecidableEq (L.Rel k)
inst✝¹ : (k : ℕ) → Encodable (L.Func k)
inst✝ : (k : ℕ) → Encodable (L.Rel k)
T : Theory L
Γ : Sequent L
nwf : ¬WellFounded (SearchTree.Lt T Γ)
A : Acc (SearchTree.Lt T Γ) ⊤
s : ℕ
Δ : Sequent L
a : SearchTreeAux T Γ s Δ
⊢ Acc (SearchTree.Lt T Γ) ⟨s, ⟨Δ, a⟩⟩
case mk.mk.zero
L : Language
inst✝³ : (k : ℕ) → DecidableEq (L.Func k)
inst✝² : (k : ℕ) → DecidableEq (L.Rel k)
inst✝¹ : (k : ℕ) → Encodable (L.Func k)
inst✝ : (k : ℕ) → Encodable (L.Rel k)
T : Theory L
Γ : Sequent L
nwf : ¬WellFounded (SearchTree.Lt T Γ)
A : Acc (SearchTree.Lt T Γ) ⊤
s : ℕ
Δ : Sequent L
⊢ Acc (SearchTree.Lt T Γ) ⟨0, ⟨Γ, SearchTreeAux.zero⟩⟩

case mk.mk.succ
L : Language
inst✝³ : (k : ℕ) → DecidableEq (L.Func k)
inst✝² : (k : ℕ) → DecidableEq (L.Rel k)
inst✝¹ : (k : ℕ) → Encodable (L.Func k)
inst✝ : (k : ℕ) → Encodable (L.Rel k)
T : Theory L
Γ : Sequent L
nwf : ¬WellFounded (SearchTree.Lt T Γ)
A : Acc (SearchTree.Lt T Γ) ⊤
s : ℕ
Δ : Sequent L
s✝ : ℕ
Δ₁✝ Δ₂✝ : Sequent L
a✝¹ : SearchTreeAux T Γ s✝ Δ₁✝
a✝ : Δ₂✝ ≺⟨s✝⟩ Δ₁✝
a_ih✝ : Acc (SearchTree.Lt T Γ) ⟨s✝, ⟨Δ₁✝, a✝¹⟩⟩
⊢ Acc (SearchTree.Lt T Γ) ⟨s✝ + 1, ⟨Δ₂✝, a✝¹.succ a✝⟩⟩