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Proof step 19 from proof max-del1 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ¬ j < i → max(j, i) = j
Proof step 21:
¬ ¬ i0 < max(ints0), i < max(i0, max(ints0)), ∀ i. i < max(ints0) → max(ints0 -1l i) = max(ints0) ⊦ max(i0, max(ints0 -1l i)) = max(i0, max(ints0)), i = i0, ints0 = [], ints0 = i '

Rule argument

spec: int-min inst: name: Max-left seq: ⊦ ¬ j < i → max(j, i) = j subst: [i, j] → [max(ints0), i0] flags: rewrite

Additional information

Used simplifier rules: max-del1-01: ⊦ ints ≠ [] → (max(ints) < max(ints -1l i) ↔ ints = i ' ∧ i < 0);%max: ⊦ max(i, j) = j ↔ ¬ j < i; from specification int-min%max-a: ⊦ max(i, max(j, j0)) = max(max(i, j), j0); from specification int-min%max-c: ⊦ max(i, j) = max(j, i); from specification int-min%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista] Used terms: max(ints0), i0