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Proof step 19 from proof prime-divides-coef (previous step)

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), j0 | fac(j) ∨ j0 | fac(j + 1) ⊦ j0 | i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j)
Proof step 21:
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

Rule argument

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

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, j0