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Proof step 6 from proof coprime-divides-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 7:
1 = i * i0 + j * j1, gcd(i, j) = 1, j0 = j0 * i * i0 + j0 * j * j1, i | j * j0 ⊦ i | j0

Rule argument

fma: j0 = j0 * i * i0 + j0 * j * j1

Additional information

Used simplifier rules: ⊦ i * j + i * j0 = i * (j + j0); (s)%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i = 1 → i * j = j; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2 Used formulas: j0 = j0 * i * i0 + j0 * j * j1