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Proof step 30 from proof max-ins-max (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a

Additional information

Used simplifier rules: transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%ls-le: ⊦ a < b → (¬ b < a ↔ true); from specification oelem%irreflexivity: ⊦ ¬ a < a; from specification oelem Used terms: a