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Proof step 11 from proof sort-max-last (previous step)

sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a, sort(x1 + x0) + a ') = (sort(x1 + x0) + a ') + a ', a < max((a ' + x1) + x0), a < max(x1 + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ordered≤(x0) ∧ ¬ a < max(x0) → ins≤(a, x0) = x0 + a '
Proof step 13:
¬(ordered≤(sort(x1 + x0) + a ') ∧ ¬ a < max(sort(x1 + x0) + a ')), sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a, sort(x1 + x0) + a ') = (sort(x1 + x0) + a ') + a ', a < max((a ' + x1) + x0), a < max(x1 + x0)

Rule argument

spec: inst: name: ins-max seq: ⊦ ordered≤(x0) ∧ ¬ a < max(x0) → ins≤(a, x0) = x0 + a ' subst: [x0, a] → [sort(x1 + x0) + a ', a] flags: rewrite, current

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: sort(x1 + x0) + a ', a