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

0 ≤ i ⊦ binom_coef(i, 0) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [0, i] flags: rewrite, current

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%fac-zero-02: ⊦ fac(i) ≠ 0;%sub-zero-01: ⊦ i - 0 = i; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%div-same: i ≠ 0 ⊦ i / i = 1; from specification int-div%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: 0, i