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Proof step 54 from proof harness-2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
x = 3 ' + 2 ' + 2 ', to4 = fail ⊦ 〈build_rec#(1; x, to4)〉〈if to4 = fail then to0 := fail else to0 := some(Node(Leaf, to4 .t))〉〈to1 := to0 ; if x ≠ [] 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 : ⊦ d ' + x = y → 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])]]