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Proof step 1 from proof coef-rec-lower (conclusion)

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

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs