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Proof step 18 from proof max-rec (previous step)

max(i ' + ints) ∈ i ' + ints, i ≤ max(i ' + ints), max(ints) ≤ max(i ' + ints), ∀ i0. i0 ∈ ints → i0 ≤ max(i ' + ints), i ∈ ints → i ≤ max(ints), ∀ i. i ∈ ints → i ≤ max(ints) ⊦ ints = [], max(i ' + ints) = max(i, max(ints)), max(i ' + ints) ∈ ints

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ i ∈ i0 ' + ints ↔ ¬ ¬(i = i0 ∨ i ∈ ints)

Rule argument

spec: list inst: intlista name: in-rec seq: ⊦ i ∈ i0 ' + ints ↔ ¬ ¬(i = i0 ∨ i ∈ ints) subst: [ints, i0, i] → [ints, i, max(i ' + ints)] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%Max-right: ⊦ j < i → max(j, i) = 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%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%max: ⊦ max(i, j) = j ↔ ¬ j < i; from specification int-min%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: ints, i, max(i ' + ints)