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Proof step 30 from proof coef-mult-rec-lower (previous step)

0 < i + 1 - j, 0 < j, (fac(i - j) * j * fac(j - 1)) * i0 = fac(i), fac(i) = (fac(j - 1) * (i + 1 - j) * fac(i + 1 - j - 1)) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: 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%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%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