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Proof step 21 from proof prime-divides-coef (previous step)

prime(j0) ∧ j < j0 ∧ 0 < j, prime(j0), (fac(j) * fac(j + 1)) * i = fac(j * 2 + 1), 0 ≤ j, 0 < j, j + 2 ≤ j0, j0 ≤ j * 2 + 1, prime(j0), false ∨ j0 | fac(j + 1) ⊦ j0 | i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
(fac(j) * fac(j + 1)) * i = fac(j * 2 + 1), j < j0, 0 ≤ j, 0 < j, j + 2 ≤ j0, j0 ≤ j * 2 + 1, prime(j0), j0 | fac(j + 1), 1 < j0, 0 < j0 ⊦ j0 | i

Rule argument

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) 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%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%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]