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Proof step 31 from proof max-ins-max (previous step)

∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ a0 < a, max(ins≤(a, a0 ' + x0)) = a, a < max(a0 ' + x0), ¬ a0 < a ∧ ordered≤(a0 ' + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ max(a ' + a0 ' + x0) = a, a0 < a, a < max(a0 ' + x0), ordered≤(a0 ' + x0), a0 < max(a0 ' + x0)

Rule argument

Additional information

Used simplifier rules: nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x; from specification olist