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Proof step 37 from proof coef-mult-rec-lower (previous step)

(fac(i - j) * j * fac(j - 1)) * i0 = fac(i), fac(j - 1) * j * i0 = i1 * fac(j - 1) * (i + 1 - j), 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)

User applied rule cut formula

And obtained the following new goals

Proof step 38:
i1 * fac(j - 1) * (i + 1 - j) = fac(j - 1) * i1 * (i + 1 - j), (fac(i - j) * j * fac(j - 1)) * i0 = fac(i), fac(j - 1) * j * i0 = i1 * fac(j - 1) * (i + 1 - j), 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)

Rule argument

fma: i1 * fac(j - 1) * (i + 1 - j) = fac(j - 1) * i1 * (i + 1 - j)

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: i1 * fac(j - 1) * (i + 1 - j) = fac(j - 1) * i1 * (i + 1 - j)