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Proof step 10 from proof min-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ¬ j < i → min(j, i) = i
Proof step 12:
¬ ¬ i < min(ints), min(i ' + ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = min(i, min(ints))
Proof step 18:
¬ i < min(ints), min(i ' + ints) ≤ i, ∀ i0. i0 ∈ ints → min(i ' + ints) ≤ i0, ∀ i. i ∈ ints → min(ints) ≤ i ⊦ ints = [], min(i ' + ints) = min(ints)

Rule argument

spec: int-min inst: name: Min-right seq: ⊦ ¬ j < i → min(j, i) = i subst: [i, j] → [min(ints), i] flags: rewrite

Additional information

Used terms: min(ints), i