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Proof step 46 from proof congmod-def-mod-02 (previous step)

i % abs(j) < 0, i < 0, i0 < 0 ⊦ i % abs(j) + abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ j ≠ 0 → i % abs(j) = i % j
Proof step 48:
j ≠ 0, i % j < 0, i < 0, i0 < 0 ⊦ i % j + abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j, j = 0

Rule argument

spec: int-div inst: name: mod-abs seq: ⊦ j ≠ 0 → i % abs(j) = i % j subst: [j, i] → [j, i] flags: rewrite

Additional information

Used terms: j, i