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Proof step 7 from proof coprime-divides-01 (previous step)

1 = i * i0 + j * j1, gcd(i, j) = 1, i | j * (j0 * i * i0 + j0 * j * j1) ⊦ i | j0 * i * i0 + j0 * j * j1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides-add seq: ⊦ i | j → (i | j + j0 ↔ i | j0) subst: [j0, j, i] → [j0 * j * j1, j0 * i * i0, i] flags: rewrite, current

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%div-mult: ⊦ i | i * j;%divides-mult-01: ⊦ i | j → i | j * j0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%dist-rmerge: ⊦ i * j + i * j0 = i * (j + j0); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2 Used terms: j0 * j * j1, j0 * i * i0, i