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Proof step 10 from proof coef-sub-mult (previous step)

j ≤ i ∧ 0 ≤ j → fac(i - j) * fac(j) | fac(i), j - 1 ≤ i ∧ 0 ≤ j - 1 → fac(i - (j - 1)) * fac(j - 1) | fac(i), 0 ≤ j - 1 ∧ j - 1 ≤ i, 0 ≤ j ∧ j ≤ i, j ≤ i, 0 < j, 0 < i ⊦ (fac(i) / (fac(i - j) * fac(j)) - fac(i) / (fac(i - (j - 1)) * fac(j - 1))) * fac(j) * fac(i + 1 - j) = fac(i) * (i + 1 - 2 * 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%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%le-add-03: ⊦ i ≤ i0 ∧ j0 ≥ 0 → i ≤ i0 + j0; from specification int-abs%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%sub-sub-04: ⊦ i - (j - j0) = i + j0 - j; from specification int-abs