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Proof step 1 from proof cong-mult (conclusion)

⊦ ≡mod(j0 * j + i, i0, j) ↔ ≡mod(i, i0, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)
Proof step 3:
¬ 0 < j ⊦ ≡mod(j0 * j + i, i0, j) ↔ ≡mod(i, i0, j)
Proof step 12:
0 < j ⊦ (j0 * j + i) |%| j = i0 |%| j ↔ ≡mod(i, i0, j)

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [j, i0, j0 * j + i] flags: rewrite, current

Additional information

Used terms: j, i0, j0 * j + i