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Proof step 19 from proof coef-fac-divides-h (previous step)

fac(j - 1) * fac(i - j) | fac(i - 1), (j * fac(j - 1)) * fac(i - 1 + j) | fac(i - 1), j < i, 0 < j, 0 ≤ j, 1 < i, 0 < i ⊦ (j * fac(j - 1)) * fac(i - j) | j * fac(i - 1), (j * fac(j - 1)) * fac(i - j) | fac(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: div-mult-01 seq: ⊦ i ≠ 0 → (i * i0 | i * i1 ↔ i0 | i1) subst: [i1, i0, i] → [fac(i - 1), fac(j - 1) * fac(i - j), j] flags: rewrite

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%fac-zero-02: ⊦ fac(i) ≠ 0;%sub-zero-01: ⊦ i - 0 = i; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%div-zero-zero: ⊦ 0 | i ↔ i = 0; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: fac(i - 1), fac(j - 1) * fac(i - j), j