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Proof step 2 from proof fac-ls-zero (previous step)

⊦ i * fac(j) < 0 ↔ i < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬(j < 0 ∧ i ≠ 0))

Rule argument

spec: int-mult inst: name: zero-ls-02 seq: ⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬(j < 0 ∧ i ≠ 0)) subst: [j, i] → [fac(j), i] flags: rewrite

Additional information

Used simplifier rules: fac-pos-01: ⊦ ¬ fac(i) ≤ 0;%fac-not-neg: ⊦ ¬ fac(i) < 0;%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-ge-01: ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 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