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Proof step 2 from proof fac-divides (previous step)

i ≤ j, 0 ≤ i, 0 ≤ j ⊦ fac(j - i) * fac(i) | fac(j)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: coef-fac-divides seq: ⊦ 0 < j ∧ j ≤ i → fac(j) * fac(i - j) | fac(i) subst: [j, i] → [i, j] flags: current, []

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%sub-zero-01: ⊦ i - 0 = i; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-zero: ⊦ i | i; from specification int-gcd Used terms: i, j