-- Mathlib/.lake/packages/lean4/src/lean/Std/Sat/AIG/CachedLemmas.lean
theorem mkGateCached.go_eval_eq_mkGate_eval {aig : AIG α} {input : GateInput aig} :
    ⟦go aig input, assign⟧ = ⟦aig.mkGate input, assign⟧

Proof state:
case h_2.h_9
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
aig : AIG α
input : aig.GateInput
x✝¹⁰ : Option (CacheHit aig.decls (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv))
heq✝ : aig.cache.get? (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv) = none
x✝⁹ x✝⁸ : Decl α
linv✝ rinv✝ : Bool
x✝⁷ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = true → False
x✝⁶ : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = false → False
x✝⁵ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.rhs.inv = true → False
x✝⁴ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.rhs.inv = false → False
x✝³ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝² : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = true → input.rhs.inv = false → False
x✝¹ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.lhs.inv = false → input.rhs.inv = true → False
⊢ ⟦assign,
      if (input.lhs.ref.gate == input.rhs.ref.gate && input.lhs.inv == false && input.rhs.inv == false) = true then
        { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
          ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }
      else
        if (input.lhs.ref.gate == input.rhs.ref.gate && input.lhs.inv == !input.rhs.inv) = true then
          { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
        else
          {
            aig :=
              { decls := aig.decls.push (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv),
                cache :=
                  Cache.insert aig.decls aig.cache
                    (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv),
                invariant := ⋯ },
            ref := { gate := aig.decls.size, hgate := ⋯ } }⟧ =
    ⟦assign, aig.mkGate input⟧

Tactic:
split

Result:
case h_2.h_9.isTrue
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
aig : AIG α
input : aig.GateInput
x✝¹⁰ : Option (CacheHit aig.decls (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv))
heq✝ : aig.cache.get? (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv) = none
x✝⁹ x✝⁸ : Decl α
linv✝ rinv✝ : Bool
x✝⁷ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = true → False
x✝⁶ : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = false → False
x✝⁵ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.rhs.inv = true → False
x✝⁴ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.rhs.inv = false → False
x✝³ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝² : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = true → input.rhs.inv = false → False
x✝¹ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.lhs.inv = false → input.rhs.inv = true → False
h✝ : (input.lhs.ref.gate == input.rhs.ref.gate && input.lhs.inv == false && input.rhs.inv == false) = true
⊢ ⟦assign,
      { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
        ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }⟧ =
    ⟦assign, aig.mkGate input⟧

case h_2.h_9.isFalse
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
aig : AIG α
input : aig.GateInput
x✝¹⁰ : Option (CacheHit aig.decls (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv))
heq✝ : aig.cache.get? (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv) = none
x✝⁹ x✝⁸ : Decl α
linv✝ rinv✝ : Bool
x✝⁷ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = true → False
x✝⁶ : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = false → False
x✝⁵ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.rhs.inv = true → False
x✝⁴ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.rhs.inv = false → False
x✝³ : aig.decls[input.lhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝² : aig.decls[input.lhs.ref.gate] = Decl.const false → input.lhs.inv = true → input.rhs.inv = false → False
x✝¹ : aig.decls[input.rhs.ref.gate] = Decl.const true → input.lhs.inv = false → input.rhs.inv = false → False
x✝ : aig.decls[input.rhs.ref.gate] = Decl.const false → input.lhs.inv = false → input.rhs.inv = true → False
h✝ : ¬(input.lhs.ref.gate == input.rhs.ref.gate && input.lhs.inv == false && input.rhs.inv == false) = true
⊢ ⟦assign,
      if (input.lhs.ref.gate == input.rhs.ref.gate && input.lhs.inv == !input.rhs.inv) = true then
        { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
      else
        {
          aig :=
            { decls := aig.decls.push (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv),
              cache :=
                Cache.insert aig.decls aig.cache
                  (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv),
              invariant := ⋯ },
          ref := { gate := aig.decls.size, hgate := ⋯ } }⟧ =
    ⟦assign, aig.mkGate input⟧