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Proof step 44 from proof coef-sub-mult (previous step)

0 < i + 1 - j, 0 ≤ i, 0 ≤ j, ((i + 1 - j) * fac(i + 1 - j - 1)) * fac(j - 1) | fac(i), fac(i - j) * j * fac(j - 1) | fac(i), 0 < j, 0 < i, j ≤ i, fac(i - j) | fac(i) * (i + 1 - j) * fac(i + 1 - j - 1) ⊦ (i + 1 - j) * fac(i + 1 - j - 1) = (j + i + 1 - 2 * j) * fac(i - j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%neq-not-zero: ⊦ i * j ≠ i * j0 → i ≠ 0; (forward) from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%div-mult: ⊦ i | i * j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; 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-add-06: ⊦ i + j - i0 + j = i - i0; from specification int-abs%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs