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Proof step 3 from proof ex-modeq-half (previous step)

odd(j), 0 < j ⊦ ≡mod(i0 |%| j, i0, j) ∧ abs(i0 |%| j) ≤ j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)
Proof step 5:
0 < j, odd(j), 0 < j ⊦ (i0 |%| j) |%| j = i0 |%| j ∧ abs(i0 |%| j) ≤ j / 2, ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2

Rule argument

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

Additional information

Used terms: j, i0, i0 |%| j