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Proof step 22 from proof prime-divides-coef (previous step)

(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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: prime-fac-divides-not seq: ⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j) subst: [j, i] → [j + 1, j0] flags: rewrite, current

Additional information

Used simplifier rules: prime-fac-divides-01: ⊦ prime(i) → i | fac(i);%zero-02: ⊦ 0 < i ∧ 0 < j → 0 < i + j; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%les: ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1); from specification int-abs%int-add-pos: ⊦ 0 ≤ j ∧ j < j1 ∧ j + i = j1 → 0 < i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%le-add: ⊦ i + j ≤ i0 + j ↔ i ≤ i0; from specification int-abs%le-same-01: ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j + 1, j0