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Proof step 3 from proof div-not-ls (previous step)

1 < j, i < j, 0 < i, 0 < j, j | i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i | j ↔ (∃ i0. i * i0 = j)

Rule argument

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

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i ↔ j < 1); (s)% ⊦ i < 1 ↔ i ≤ 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: i, j