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Proof step 24 from proof max-ins (previous step)

max(ins≤(a, x0)) < a0, a0 < a, ∀ a1. max(ins≤(a1, x0)) = max(x0) ∨ max(x0) < a1 ⊦ x0 = [], (max(ins≤(a, x0)) < a0 ⊃ a0;max(ins≤(a, x0))) = max(x0), max(x0) < a0, max(x0) < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
max(ins≤(a, x0)) < a0, a0 < a, max(ins≤(a, x0)) < a, ∀ a1. max(ins≤(a1, x0)) = max(x0) ∨ max(x0) < a1 ⊦ x0 = [], max(x0) < a0, max(x0) < a

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem