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Proof step 16 from proof min-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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: min-in-not-ls: ⊦ i ∈ ints → ¬ i < min(ints); Used terms: ints, i, min(i ' + ints)