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Proof step 53 from proof harness-1 (previous step)

x1 = 3 ' + 3 ' + 2 ', to3 = fail, x0 = x1 ∧ d0 = 2, h0 = head(x0), to2 = fail, to4 = fail ⊦ 〈build_rec#(d0 + 1; x0, to4)〉〈if to4 = fail then to := fail else { build_rec#(d0 + 1; x0, to2) ; if to2 = fail then to := fail else to := some(Node(to4 .t, to2 .t)) }〉〈to3 := to, x1 := x0 ; if to3 = fail then to := fail else { to2 := fail ; build_rec#(2; x1, to2) ; if to2 = fail then to := fail else to := some(Node(to3 .t, to2 .t)) }〉〈to4 := to ; if to4 = fail then to0 := fail else to0 := some(Node(Leaf, to4 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = some(Node(Leaf, Node(Node(Leaf, Leaf), Leaf)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
x0 = 3 ' + 3 ' + 2 ', to4 = fail ⊦ 〈build_rec#(3; x0, to4)〉〈if to4 = fail then to := fail else { to2 := fail ; build_rec#(3; x0, to2) ; if to2 = fail then to := fail else to := some(Node(to4 .t, to2 .t)) }〉〈to3 := to, x1 := x0 ; if to3 = fail then to := fail else { to2 := fail ; build_rec#(2; x1, to2) ; if to2 = fail then to := fail else to := some(Node(to3 .t, to2 .t)) }〉〈to4 := to ; if to4 = fail then to0 := fail else to0 := some(Node(Leaf, to4 .t))〉〈to1 := to0 ; if x1 ≠ [] then to1 := fail〉 to1 = some(Node(Leaf, Node(Node(Leaf, Leaf), Leaf)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ d0 ' ↔ d = d0], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPFORWARD : ⊦ d ' + x = y → d ∈ y], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPFORWARD : ⊦ x + d ' = y → d ∈ y])]]