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Proof step 7 from proof middle-coef-divides-not (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%le-same-01: ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j); from specification int-mult