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Proof step 3 from proof prime-divides-01 (previous step)

1 < i, j0 < i, 0 < j0, 0 < i, prime(i), j0 | j, i | j ⊦ i | j / j0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [j, j0] flags: <all paths>

Additional information

Used simplifier rules: prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0);%div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i;%j ≠ 0 ⊦ (i * j) / j = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, j0