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Proof step 4 from proof cong-mult (previous step)

j ≤ 0 ⊦ ≡mod(j0 * j + i, i0, j) ↔ ≡mod(i, i0, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 6:
j ≤ 0 ⊦ j | abs(j0 * j + i - i0) ↔ ≡mod(i, i0, j)

Rule argument

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

Additional information

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