Theorem: BVExpr.bitblast.go_denote_mem_prefix (LeanSAT/Reflect/BVExpr/BitBlast/Lemmas/Expr.lean)

State before:
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ start < (go aig expr).val.aig.decls.size
Tactic:
apply Nat.lt_of_lt_of_le
State after:
case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ start < ?m

case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ?m ≤ (go aig expr).val.aig.decls.size

case m
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ Nat

State before:
case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ start < ?m

case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ?m ≤ (go aig expr).val.aig.decls.size

case m
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ Nat
Tactic:
exact hstart
State after:
case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ aig.decls.size ≤ (go aig expr).val.aig.decls.size

State before:
case a
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ aig.decls.size ≤ (go aig expr).val.aig.decls.size
Tactic:
apply (go aig expr).property
State after:
no goals

State before:
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ⟦{ aig := (go aig expr).val.aig, ref := { gate := start, hgate := ⋯ } }, assign.toAIGAssignment⟧ =
    ⟦{ aig := aig, ref := { gate := start, hgate := hstart } }, assign.toAIGAssignment⟧
Tactic:
apply denote.eq_of_aig_eq (entry := ⟨aig, start,hstart⟩)
State after:
case hprefix
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ IsPrefix { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls (go aig expr).val.aig.decls

State before:
case hprefix
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ IsPrefix { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls (go aig expr).val.aig.decls
Tactic:
apply IsPrefix.of
State after:
case hprefix.idx_eq
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ∀ (idx : Nat) (h : idx < { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size),
    (go aig expr).val.aig.decls[idx] = { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls[idx]

case hprefix.size_le
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size ≤ (go aig expr).val.aig.decls.size

State before:
case hprefix.idx_eq
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ∀ (idx : Nat) (h : idx < { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size),
    (go aig expr).val.aig.decls[idx] = { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls[idx]

case hprefix.size_le
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size ≤ (go aig expr).val.aig.decls.size
Tactic:
. intros
  apply go_decl_eq
State after:
case hprefix.size_le
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size ≤ (go aig expr).val.aig.decls.size

State before:
case hprefix.size_le
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size ≤ (go aig expr).val.aig.decls.size
Tactic:
. intros
  apply (go aig expr).property
State after:
no goals

State before:
case hprefix.idx_eq
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ ∀ (idx : Nat) (h : idx < { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size),
    (go aig expr).val.aig.decls[idx] = { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls[idx]
Tactic:
intros
State after:
case hprefix.idx_eq
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
idx✝ : Nat
h✝ : idx✝ < { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size
⊢ (go aig expr).val.aig.decls[idx✝] = { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls[idx✝]

State before:
case hprefix.idx_eq
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
idx✝ : Nat
h✝ : idx✝ < { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size
⊢ (go aig expr).val.aig.decls[idx✝] = { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls[idx✝]
Tactic:
apply go_decl_eq
State after:
no goals

State before:
case hprefix.size_le
w : Nat
aig : AIG BVBit
expr : BVExpr w
assign : Assignment
start : Nat
hstart : start < aig.decls.size
⊢ { aig := aig, ref := { gate := start, hgate := hstart } }.aig.decls.size ≤ (go aig expr).val.aig.decls.size
Tactic:
apply (go aig expr).property
State after:
no goals