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Proof step 2 from proof product-min-nlz (previous step)

Π(ints -l i0) < 0, Π(ints -l i0) < min(i ' + ints), 0 < min(i ' + ints) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ min(ints) → ¬ Π ints < 0

Rule argument

spec: inst: name: product-min-not-ls-zero seq: ⊦ 0 ≤ min(ints) → ¬ Π ints < 0 subst: [ints] → [ints -l i0] flags: rewrite, current

Additional information

Used simplifier rules: min-del-nlz: ⊦ 0 < min(i ' + ints) → ¬ min(ints -l i0) < 0;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista] Used terms: ints -l i0