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Proof step 2 from proof coef-one (previous step)

0 < i ⊦ binom_coef(i, 1) = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ j ∧ j ≤ i → binom_coef(i, j) = fac(i) / (fac(i - j) * fac(j))
Proof step 4:
0 ≤ 1 ∧ 1 ≤ i, 0 < i ⊦ fac(i) / (fac(i - 1) * fac(1)) = i

Rule argument

spec: int-fac inst: name: binom-def seq: ⊦ 0 ≤ j ∧ j ≤ i → binom_coef(i, j) = fac(i) / (fac(i - j) * fac(j)) subst: [j, i] → [1, i] flags: rewrite, current

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs Used terms: 1, i