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Proof step 25 from proof max-ins-max (previous step)

a1 < a, a0 < a, max(a1 ' + ins≤(a, y)) < a0, max(a1 ' + ins≤(a, y)) < a, ∀ a2. max(ins≤(a2, a1 ' + y)) = a2 ∨ a2 < max(a1 ' + y) ⊦ a0 = a, a < (max(a1 ' + y) < a0 ⊃ a0;max(a1 ' + y))

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: a

Additional information

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