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Proof step 26 from proof harness-2 (previous step)

x0 = 3 ' + 2 ' + 2 ', to4 = fail, x2 = x0 ∧ d0 = 3, h0 = head(x2), to5 = some(Leaf) ∧ x = pop(x2), to6 = fail ⊦ 〈build_rec#(3; x, to6)〉〈if to6 = fail then to := fail else to := some(Node(to5 .t, to6 .t))〉〈to3 := to, x1 := x ; if to3 = fail then to := fail else { to6 := fail ; build_rec#(2; x1, to6) ; if to6 = fail then to := fail else to := some(Node(to3 .t, to6 .t)) }〉〈to5 := to ; if to5 = fail then to0 := fail else to0 := some(Node(Leaf, to5 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = fail

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
x = 2 ' + 2 ', to6 = fail ⊦ 〈build_rec#(3; x, to6)〉〈if to6 = fail then to := fail else to := some(Node(Leaf, to6 .t))〉〈to3 := to, x1 := x ; if to3 = fail then to := fail else { to6 := fail ; build_rec#(2; x1, to6) ; if to6 = fail then to := fail else to := some(Node(to3 .t, to6 .t)) }〉〈to5 := to ; if to5 = fail then to0 := fail else to0 := some(Node(Leaf, to5 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = fail

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ d0 ' ↔ d = d0], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPFORWARD : ⊦ x + d ' = y → d ∈ y], [CSIMPSEQ : ⊦ some(t) .t = t], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ pop(d ' + x) = x])]]