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Proof step 7 from proof coef-fac-divides (previous step)

0 < j, j < i, 1 < i, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ j - 1 ≤ i - 1 ∧ 0 < j - 1 ∧ 0 < i - 1, i = j, fac(j) * fac(i - j) | fac(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-one: ⊦ fac(1) = 1;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs