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Proof step 7 from proof coef-eq-zero (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j | i ∧ j ≠ 0 → (i / j = i0 ↔ i = i0 * j)
Proof step 9:
¬(fac(i - j) * fac(j) | fac(i) ∧ fac(i - j) * fac(j) ≠ 0), fac(i) / (fac(i - j) * fac(j)) = 0, 0 ≤ i, 0 ≤ j, j ≤ i ⊦

Rule argument

spec: int-gcd inst: name: div-eq seq: ⊦ j | i ∧ j ≠ 0 → (i / j = i0 ↔ i = i0 * j) subst: [i0, j, i] → [0, fac(i - j) * fac(j), fac(i)] flags: rewrite

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 0, fac(i - j) * fac(j), fac(i)