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Proof step 10 from proof max-del1-01 (previous step)

i0 < max(i0 ' + (ints0 -1l i)), max(ints0) < max(i0 ' + (ints0 -1l i)), ∀ i1. max(ints0) < max(ints0 -1l i1) → ints0 = i1 ' ∧ i1 < 0 ⊦ i = i0, i0 ' + ints0 = i ', ints0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: max-one: ⊦ max(i ') = i;%del1-empty: ⊦ ints ≠ [] → (ints -1l i = [] ↔ ints = i '); from specification list-del[intlista]%one-01: ⊦ ints ≠ [] → (i ' = ints0 + ints ↔ ints0 = [] ∧ i ' = ints); from specification list[intlista]%e: ⊦ i ' ≠ []; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%one-01: ⊦ i ' -1l i = []; from specification list-del[intlista]%app: ⊦ ints + [] = ints; from specification list[intlista]%irreflexivity: ⊦ ¬ i < i; from specification oelem[intlista] Used terms: ints0 -1l i, i0