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Proof step 2 from proof max-ins-max-last-sort (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ a < max(x0) ∧ ordered≤(x0) → ins≤(a, x0) = x0 + a '
Proof step 4:
¬(¬ a < max(sort(x0)) ∧ ordered≤(sort(x0))) ⊦ ins≤(a, sort(x0)) = sort(x0) + a ', a < max(x0)

Rule argument

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

Additional information

Used terms: sort(x0), a