Theorem: BVExpr.bitblast.blastAdd.go_decl_eq
Proof state before:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ (mkFullAdderOut aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls[idx✝] =
    aig.decls[idx✝]

case isTrue.h1
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ < (mkFullAdderOut aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls.size

case isTrue.h2
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ <
    (mkFullAdderCarry (mkFullAdderOut aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig
            ({ lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }.cast ⋯)).aig.decls.size
Tactic:
rw [AIG.LawfulOperator.decl_eq (f := mkFullAdderOut)]
Proof state after:
case isTrue.h2
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ < (mkFullAdderOut aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls.size

case isTrue.h2
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ <
    (mkFullAdderCarry (mkFullAdderOut aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig
            ({ lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }.cast ⋯)).aig.decls.size