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Proof step 36 from proof soundness (previous step)

x2 = x ⊦ 〈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 lemma

And obtained the following new goals

Proof step 2:
x ≠ [], x = x0, i ≤ j, max(x) ≤ j ⊦ 〈build_rec#(i; x, to)〉 (to ≠ fail → x0 = depths(to .t, i) + x)
Proof step 29:
x2 = x, x = [] ∨ x ≠ x ∨ ¬ 0 ≤ max(x) ∨ ¬ max(x) ≤ max(x) ⊦ 〈build_rec#(0; x, to)〉〈to0 := to, x0 := x ; if x0 ≠ [] then to0 := fail〉 (to0 ≠ fail → x2 = depths(to0 .t, 0))
Proof step 35:
〈x1 := x〉〈build_rec#(0; x, to)〉 (to ≠ fail → x1 = depths(to .t, 0) + x), x2 = 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: instance-name: lemma-name: soundness-rec antecedent: x ≠ [], x = x0, i ≤ j, max(x) ≤ j succedent: 〈build_rec#(i; x, to)〉 (to ≠ fail → x0 = depths(to .t, i) + x) substlist: [x, x0, i, j, to] → [x, x, 0, max(x), to] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (x, x, 0, max(x), to)]]