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Proof step 13 from proof max-ins-max-last (previous step)

ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ max(x) < a0, a ' + a0 ' + x = (a0 ' + x) + a ', x = [], a < (max(x) < a0 ⊃ a0;max(x)), a0 < a, a0 < (max(x) < a0 ⊃ a0;max(x))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
ordered≤(max(x) ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ max(x) ' + x = x + max(x) ', x = []

Rule argument

Additional information

Used simplifier rules: irreflexivity: ⊦ ¬ a < a; from specification oelem%a: ⊦ (x + y) + z = x + y + z; from specification list%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; from specification list%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem%seq: ⊦ ¬ b < a → (¬ a < b ↔ a = b); from specification oelem