rcases c with ⟨⟨⟩, Γ⟩ <;> simp[isProper, F, Code.equiv, Bool.and_assoc]
case cons
μ : Type ?u.175455
L : Language
inst✝⁶ : (k : ℕ) → DecidableEq (L.Func k)
inst✝⁵ : (k : ℕ) → DecidableEq (L.Rel k)
inst✝⁴ : (k : ℕ) → Primcodable (L.Func k)
inst✝³ : (k : ℕ) → Primcodable (L.Rel k)
inst✝² : UniformlyPrimcodable L.Func
inst✝¹ : UniformlyPrimcodable L.Rel
inst✝ : Primcodable μ
this✝ : Primrec₂ fun x p => p.2.2 && LO.FirstOrder.Derivation.ProofList.F p.1.2 (sequents p.2.1) p.1.1
this :
  Primrec fun l => List.rec true (fun c l' ih => ih && LO.FirstOrder.Derivation.ProofList.F c.2 (sequents l') c.1) l
c : Code L × List (SyntacticFormula L)
l : List (Code L × List (SyntacticFormula L))
ih : List.rec true (fun c l' ih => ih && LO.FirstOrder.Derivation.ProofList.F c.2 (sequents l') c.1) l = isProper l
⊢ (isProper l && LO.FirstOrder.Derivation.ProofList.F c.2 (sequents l) c.1) = isProper (c :: l)
no goals