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Proof step 45 from proof coef-sub-mult (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: eq-nonzero-01 seq: ⊦ i ≠ 0 → (j * i = j0 * i ↔ j = j0) subst: [j0, i, j] → [j + i + 1 - 2 * j, fac(i - j), i + 1 - j] flags: rewrite

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-add: ⊦ i + j - i = j; from specification int-abs%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2 Used terms: j + i + 1 - 2 * j, fac(i - j), i + 1 - j