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Proof step 12 from proof max-ins-max-last (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: a0

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%cons-03: ⊦ ordered≤(a ' + x) → ins≤(a, x) = a ' + x; from specification olist%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%irreflexivity: ⊦ ¬ a < a; from specification oelem Used terms: a0