-- Mathlib/.lake/packages/lean4/src/lean/Std/Sat/AIG/CachedLemmas.lean
theorem mkGateCached.go_le_size (aig : AIG α) (input : GateInput aig) :
    aig.decls.size ≤ (go aig input).aig.decls.size

Proof state:
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
input : aig.GateInput
⊢ aig.decls.size ≤
    (match aig.cache.get? (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv) with
          | some hit =>
            { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
              ref := { gate := hit.idx, hgate := ⋯ } }
          | none =>
            match aig.decls[input.lhs.ref.gate], aig.decls[input.rhs.ref.gate], input.lhs.inv, input.rhs.inv with
            | Decl.const true, x, true, x_1 =>
              { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
            | Decl.const false, x, false, x_1 =>
              { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
            | x, Decl.const true, x_1, true =>
              { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
            | x, Decl.const false, x_1, false =>
              { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
            | Decl.const true, x, false, false =>
              { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
                ref := { gate := input.rhs.ref.gate, hgate := ⋯ } }
            | Decl.const false, x, true, false =>
              { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
                ref := { gate := input.rhs.ref.gate, hgate := ⋯ } }
            | x, Decl.const true, false, false =>
              { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
                ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }
            | x, Decl.const false, false, true =>
              { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
                ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }
            | x, x_1, x_2, x_3 =>
              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 := ⋯ } }).aig.decls.size

Tactic:
split

Result:
case h_1
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
input : aig.GateInput
x✝ : Option (CacheHit aig.decls (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv))
hit✝ : 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) = some hit✝
⊢ aig.decls.size ≤
    { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
            ref := { gate := hit✝.idx, hgate := ⋯ } }.aig.decls.size

case h_2
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
input : aig.GateInput
x✝ : 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
⊢ aig.decls.size ≤
    (match aig.decls[input.lhs.ref.gate], aig.decls[input.rhs.ref.gate], input.lhs.inv, input.rhs.inv with
          | Decl.const true, x, true, x_1 =>
            { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
          | Decl.const false, x, false, x_1 =>
            { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
          | x, Decl.const true, x_1, true =>
            { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
          | x, Decl.const false, x_1, false =>
            { decls := aig.decls, cache := aig.cache, invariant := ⋯ }.mkConstCached false
          | Decl.const true, x, false, false =>
            { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
              ref := { gate := input.rhs.ref.gate, hgate := ⋯ } }
          | Decl.const false, x, true, false =>
            { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
              ref := { gate := input.rhs.ref.gate, hgate := ⋯ } }
          | x, Decl.const true, false, false =>
            { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
              ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }
          | x, Decl.const false, false, true =>
            { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
              ref := { gate := input.lhs.ref.gate, hgate := ⋯ } }
          | x, x_1, x_2, x_3 =>
            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 := ⋯ } }).aig.decls.size

Proof state:
case h_1
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
input : aig.GateInput
x✝ : Option (CacheHit aig.decls (Decl.gate input.lhs.ref.gate input.rhs.ref.gate input.lhs.inv input.rhs.inv))
hit✝ : 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) = some hit✝
⊢ aig.decls.size ≤
    { aig := { decls := aig.decls, cache := aig.cache, invariant := ⋯ },
            ref := { gate := hit✝.idx, hgate := ⋯ } }.aig.decls.size

Tactic:
simp

Result:
no goals