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Proof step 9 from proof coef-eq-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
fac(i) / (fac(i - j) * fac(j)) = 0, 0 ≤ i, 0 ≤ j, j ≤ i ⊦ fac(i - j) * fac(j) | fac(i)

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