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Proof step 1 from proof fac-le-zero (conclusion)

⊦ i * fac(j) ≤ 0 ↔ i ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0)

Rule argument

spec: int-mult inst: name: zero-le seq: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0) subst: [j, i] → [fac(j), i] flags: rewrite

Additional information

Used simplifier rules: fac-not-neg: ⊦ ¬ fac(i) < 0;%fac-pos-01: ⊦ ¬ fac(i) ≤ 0;%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: fac(j), i