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Proof step 22 from proof ins-max (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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: ⊦ ¬ a < a; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem% ⊦ ¬ b < a → (a < b ↔ a ≠ b); (ss)