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Proof step 4 from proof coef-fac-divides (previous step)

0 < i, 0 < j, j ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ fac(j) * fac(i - j) | fac(i)

User applied rule cut formula

And obtained the following new goals

Proof step 5:
0 < i, 0 < j, j ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ i = j, fac(j) * fac(i - j) | fac(i)

Rule argument

fma: i = j

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%ler: ⊦ i ≤ i; from specification int-abs%sub-sub-03: ⊦ i - i = 0; 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-zero: ⊦ i | i; from specification int-gcd Used formulas: i = j