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Proof step 1 from proof coef-sub (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
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)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs