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Proof step 28 from proof sort-max-last (previous step)

x1 + x0 ≠ [], sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ a0 = a, ins≤(a0, sort(x1 + x0) + a ') = ins≤(a0, sort(x1 + x0)) + a ', a < (max(x1 + x0) < a0 ⊃ a0;max(x1 + x0)), a < max(x1 + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
sort(x1 + a ' + x0) = sort(x1 + x0) + a ', a0 < a ⊦ x1 + x0 = [], ins≤(a0, sort(x1 + x0) + a ') = ins≤(a0, sort(x1 + x0)) + a ', a0 = a, a < max(x1 + x0)

Rule argument

Additional information

Used simplifier rules: sls: ⊦ a ≠ b → (¬ a < b ↔ b < a); from specification oelem%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%ins-less-last: ⊦ ¬ a0 < a → ins≤(a, x + a0 ') = ins≤(a, x) + a0 '; from specification olist%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem