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Proof step 4 from proof coprime-mod-zero (previous step)

gcd(j, i) = 1 ∧ j | i * i0 → j | i0, (i * i0) % j = 0, gcd(i, j) = 1 ⊦ j = 0, i0 % j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
(i * i0) % j = 0, gcd(i, j) = 1, j | i * i0 → j | i0 ⊦ j = 0, i0 % j = 0

Rule argument

Additional information

Used simplifier rules: gcd-com: ⊦ gcd(i, j) = gcd(j, i);