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Proof step 4 from proof max-del1 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≠ i0 → (i0 ' + ints) -1l i = i0 ' + (ints -1l i)
Proof step 6:
¬ i ≠ i0, i < max(i0 ' + ints0), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ max((i0 ' + ints0) -1l i) = max(i0 ' + ints0)
Proof step 9:
i ≠ i0, i < max(i0 ' + ints0), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ max(i0 ' + (ints0 -1l i)) = max(i0 ' + ints0)

Rule argument

spec: list-del inst: intlista name: del1-n seq: ⊦ i ≠ i0 → (i0 ' + ints) -1l i = i0 ' + (ints -1l i) subst: [i, ints, i0] → [i, ints0, i0] flags: rewrite

Additional information

Used terms: i, ints0, i0