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Proof step 5 from proof coef-sub (previous step)

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

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-01: j ≠ 0, i0 ≠ 0 ⊦ (i * i0) / (j * i0) = i / j; from specification int-div%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%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2