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Proof step 2 from proof coprime-mod-zero (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ gcd(i, j) = 1 ∧ i | j * j0 → i | j0
Proof step 4:
gcd(j, i) = 1 ∧ j | i * i0 → j | i0, (i * i0) % j = 0, gcd(i, j) = 1 ⊦ j = 0, i0 % j = 0

Rule argument

spec: inst: name: coprime-divides-01 seq: ⊦ gcd(i, j) = 1 ∧ i | j * j0 → i | j0 subst: [i, j, j0] → [j, i, i0] flags: current, []

Additional information

Used terms: j, i, i0