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Proof step 7 from proof max-del1-01 (previous step)

max(i0 ' + ints0) < max(i0 ' + (ints0 -1l i)), ∀ i. max(ints0) < max(ints0 -1l i) → ints0 = [] ∨ ints0 = i ' ∧ i < 0 ⊦ i = i0, i0 ' + ints0 = i '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ints ≠ [] ∧ ints0 ≠ [] → max(ints + ints0) = max(max(ints), max(ints0))
Proof step 9:
i0 ' ≠ [] ∧ ints0 ≠ [], max(max(i0 '), max(ints0)) < max(i0 ' + (ints0 -1l i)), ∀ i. max(ints0) < max(ints0 -1l i) → ints0 = [] ∨ ints0 = i ' ∧ i < 0 ⊦ i = i0, i0 ' + ints0 = i '

Rule argument

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

Additional information

Used simplifier rules: max-one: ⊦ max(i ') = i;%e: ⊦ i ' ≠ []; from specification list[intlista]%c-03: ⊦ i ' = i0 ' + ints ↔ i = i0 ∧ ints = []; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%app: ⊦ ints + [] = ints; from specification list[intlista]%del1-e: ⊦ [] -1l i = []; from specification list-del[intlista]%irreflexivity: ⊦ ¬ i < i; from specification oelem[intlista] Used terms: ints0, i0 '