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Proof step 26 from proof coef-sub-mult (previous step)

(fac(i - j) * fac(j)) * i0 = fac(i), 0 ≤ i, 0 ≤ j, fac(i + 1 - j) * fac(j - 1) | fac(i), 0 < j, 0 < i, j ≤ i ⊦ (fac(i) * fac(i + 1 - j)) / fac(i - j) = fac(i) * (i + 1 - 2 * j) + (fac(i) * fac(j)) / fac(j - 1), fac(i - j) | fac(i) * fac(i + 1 - j)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: rotate, discard

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%div-mult: ⊦ i | i * j; from specification int-gcd