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Proof step 25 from proof prime-divides-coef (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: prime-fac-divides seq: ⊦ prime(i) ∧ i < j ∧ 0 < j → i | fac(j) subst: [j, i] → [j * 2 + 1, j0] flags: rewrite, current

Additional information

Used simplifier rules: prime-fac-divides-01: ⊦ prime(i) → i | fac(i);%succ-02: ⊦ i < j + 1 ↔ i ≤ j; 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%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ 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%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%les: ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1); from specification int-abs%numle-01: ⊦ i + (* j) ≤ i0 + (* j0) ↔ i ≤ i0 + (j0 - j); from specification int-abs%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%numle-08: ⊦ i + j ≤ (* i1) * i ↔ j ≤ (i1 - 1) * i; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%numls-01: ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult Used terms: j * 2 + 1, j0