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Proof step 26 from proof soundness (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
⊦ i ∈ x → i ≤ max(x)
Proof step 25:
x2 = x, x ≠ [], max(x) < 0, head(x) ∈ x → head(x) ≤ max(x) ⊦ 〈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: build-base instance-name: lemma-name: max-ge antecedent: succedent: i ∈ x → i ≤ max(x) substlist: [i, x] → [head(x), x] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (head(x), x)]]