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Proof step 12 from proof middle-coef-divides-not (previous step)

(fac(2 * i - i) * fac(i)) * i0 = fac(2 * i), 0 ≤ i, 0 < i, prime(j), 2 * i < j, j | ((fac(2 * i - i) * fac(i)) * i0) / (fac(2 * i - i) * fac(i)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
j ≠ 0 ⊦ (j * i) / j = i
Proof step 14:
fac(2 * i - i) * fac(i) ≠ 0, (fac(2 * i - i) * fac(i)) * i0 = fac(2 * i), 0 ≤ i, 0 < i, prime(j), 2 * i < j, j | i0 ⊦

Rule argument

spec: int-div inst: name: div-mult seq: j ≠ 0 ⊦ (j * i) / j = i subst: [i, j] → [i0, fac(2 * i - i) * fac(i)] flags: rewrite

Additional information

Used simplifier rules: fac-not-zero: ⊦ fac(i) * fac(j) ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, fac(2 * i - i) * fac(i)