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Proof step 10 from proof max-del1 (previous step)

i < max(i0 ' + ints0), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ i = i0, max(i0 ' + (ints0 -1l i)) = max(i0 ' + ints0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ints ≠ [] → max(i ' + ints) = max(i, max(ints))
Proof step 12:
¬ ints0 -1l i ≠ [], i < max(i0 ' + ints0), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ i = i0, max(i0 ' + (ints0 -1l i)) = max(i0 ' + ints0)
Proof step 15:
ints0 -1l i ≠ [], i < max(i0 ' + ints0), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ i = i0, max(i0, max(ints0 -1l i)) = max(i0 ' + ints0)

Rule argument

spec: inst: name: max-rec seq: ⊦ ints ≠ [] → max(i ' + ints) = max(i, max(ints)) subst: [ints, i] → [ints0 -1l i, i0] flags: rewrite, current

Additional information

Used terms: ints0 -1l i, i0