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Proof step 3 from proof max-ins-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
max(a0 ' + x0) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, a0 ' + x0).last = a

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list