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Proof step 10 from proof coef-rec-add-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 ≤ j, 0 ≤ i, 0 < j, j ≤ i, j < i, 1 < i, 0 < i ⊦ fac(i) / (fac(i - j) * fac(j)) = fac(i - 1) / (fac(i - j) * fac(j - 1)) + fac(i - 1) / (fac(i - 1 + j) * fac(j))

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%succ-01: ⊦ i + 1 ≤ j ↔ i < j; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs