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Proof step 24 from proof soundness (previous step)

x2 = x, x ≠ [], max(x) < 0, head(x) ≤ max(x), head(x) < 0 ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 ≠ fail → x2 = depths(to0 .t, 0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
x2 = x, x ≠ [], max(x) < 0, d ≤ max(x), d < 0, x = d + y ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 ≠ fail → x2 = depths(to0 .t, 0))

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: intlist lemma-name: elim-list-c antecedent: x ≠ [] succedent: d = head(x) ∧ y = pop(x) ↔ x = d + y substlist: [x, d, y] → [x, d, y] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : x ≠ [] ⊦ d = head(x) ∧ y = pop(x) ↔ x = d + y])], [EXTRATERMS : (x, d, y)]]