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Proof step 4 from proof coef-switch (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [i - j, i] flags: rewrite, current

Additional information

Used simplifier rules: sub-sub-04: ⊦ i - (j - j0) = i + j0 - j; from specification int-abs%sub-add: ⊦ i + j - i = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs%lep: ⊦ i ≤ i + j ↔ 0 ≤ j; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i - j, i