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Proof step 4 from proof coef-mult-rec-lower (previous step)

j ≤ i ∧ 0 ≤ j → fac(i - j) * fac(j) | fac(i), j ≤ i, 0 < j, 0 < i ⊦ binom_coef(i, j) * j = binom_coef(i, j - 1) * (i + 1 - j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs