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Proof step 17 from proof min-del-nlz-01 (previous step)

0 < min(i, min(ints0)), 0 < min(ints0), min(i, min(ints0 -l i0)) < 0, min(i, min(ints0 -l i0)) < min(i, min(ints0)), min(i, min(ints0 -l i0)) < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = [], i0 = i, ints0 -l i0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ¬ j < i → min(j, i) = i
Proof step 19:
¬ i < min(ints0 -l i0), 0 < min(i, min(ints0)), 0 < min(ints0), min(ints0 -l i0) < 0, min(ints0 -l i0) < min(i, min(ints0)), min(ints0 -l i0) < min(ints0), ∀ i0. ¬ min(ints0 -l i0) < 0 ⊦ ints0 = [], i0 = i, ints0 -l i0 = []

Rule argument

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

Additional information

Used simplifier rules: Min-left: ⊦ j < i → min(j, i) = j; from specification int-min%min-a: ⊦ min(i, min(j, j0)) = min(min(i, j), j0); from specification int-min%min-c: ⊦ min(i, j) = min(j, i); from specification int-min%min-03: ⊦ ¬ i < min(i, j); from specification int-min Used terms: min(ints0 -l i0), i