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Proof step 4 from proof max-ins-last (previous step)

max(a0 ' + x0) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, a0 ' + x0).last = a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x))
Proof step 6:
x0 ≠ [], (max(x0) < a0 ⊃ a0;max(x0)) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, a0 ' + x0).last = a

Rule argument

spec: inst: name: max-rec seq: ⊦ x ≠ [] → max(a ' + x) = (max(x) < a ⊃ a;max(x)) subst: [x, a] → [x0, a0] flags: rewrite, current

Additional information

Used simplifier rules: max-base: ⊦ max(a ') = a;%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%ins-one: ⊦ b < a → ins≤(a, b ') = b ' + a '; from specification olist%last-def: ⊦ (x + a ').last = a; from specification list-last Used terms: x0, a0