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Proof step 22 from proof max-perm (previous step)

i < max(ints0 -1l i), i ∈ ints0, perm(ints1, ints0 -1l i), max(ints0) ≤ i, max(ints0) < max(ints0 -1l i) ⊦ ints1 = [], max(ints0 -1l i) = max(ints0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ ints ≠ [] → (max(ints) < max(ints -1l i) ↔ ints = i ' ∧ i < 0)

Rule argument

spec: inst: name: max-del1-01 seq: ⊦ ints ≠ [] → (max(ints) < max(ints -1l i) ↔ ints = i ' ∧ i < 0) subst: [i, ints] → [i, ints0] flags: rewrite, current

Additional information

Used simplifier rules: max-empty: ⊦ max([]) = 0;%max-empty: ⊦ max([]) = 0;%max-one: ⊦ max(i ') = i;%one-01: ⊦ i ' -1l i = []; from specification list-del[intlista]%e: ⊦ i ' ≠ []; from specification list[intlista]%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%empty: ⊦ perm(ints, []) ↔ ints = []; from specification list-perm[intlista]%del1-e: ⊦ [] -1l i = []; from specification list-del[intlista] Used terms: i, ints0