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Proof step 11 from proof coef-mult-rec (previous step)

¬(fac(i - j) * j * fac(j - 1) | fac(i) ∧ fac(i - j) * j * fac(j - 1) ≠ 0), 0 < j, 0 < i, 0 < j, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i * fac(i - 1) / (fac(i - j) * fac(j - 1)) = j * fac(i) / (fac(i - j) * j * fac(j - 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-not-zero: ⊦ fac(i) * fac(j) ≠ 0;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult