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

j ≤ i, 0 ≤ j, 0 ≤ i ⊦ binom_coef(i, j) = binom_coef(i, i - j)

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 ≤ j ∧ j ≤ i, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ fac(i) / (fac(i - j) * fac(j)) = binom_coef(i, i - j)

Rule argument

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

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j, i