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Proof step 24 from proof min-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ 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, min(i ' + ints)] flags: rewrite

Additional information

Used simplifier rules: transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: ints, i, min(i ' + ints)