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Proof step 2 from proof congmod-def-mod-01 (previous step)

0 ≤ i, 0 ≤ i0 ⊦ ≡mod(i, i0, j) ↔ i |%| j = i0 |%| j, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ≡mod(i, i0, j) ↔ ≡mod(i, i0, abs(j))
Proof step 4:
0 ≤ i, 0 ≤ i0 ⊦ ≡mod(i, i0, abs(j)) ↔ i |%| j = i0 |%| j, j = 0

Rule argument

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

Additional information

Used terms: j, i0, i