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Proof step 8 from proof coef-nls-zero (previous step)

fac(i) / (fac(i - j) * fac(j)) < 0, 0 ≤ i, 0 ≤ j, j ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i ∧ 0 < j → ¬ i / j < 0

Rule argument

spec: int-div inst: name: div-zero-nls seq: ⊦ 0 ≤ i ∧ 0 < j → ¬ i / j < 0 subst: [j, i] → [fac(i - j) * fac(j), fac(i)] flags: rewrite

Additional information

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