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Proof step 4 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 ⊦ i0 ' + ints0 = i ' ∧ i < 0

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: max-app-ls: ⊦ max(ints1 + ints0) < max(ints0) ↔ ints0 = [] ∧ max(ints1) < 0;%max-one: ⊦ max(i ') = i;%del1-y: ⊦ (i ' + ints) -1l i = ints; from specification list-del[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c-03: ⊦ i ' = i0 ' + ints ↔ i = i0 ∧ ints = []; from specification list[intlista]%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: i, ints0, i0