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Proof step 12 from proof congmod-def-mod-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 0 ≤ i % j → i |%| j = i % j
Proof step 14:
¬ 0 ≤ i % j, 0 ≤ i % abs(j), 0 ≤ i % abs(j), i0 < 0, i < 0 ⊦ j = 0, i % abs(j) = i0 |%| abs(j) ↔ i |%| j = i0 |%| j
Proof step 17:
0 ≤ i % j, 0 ≤ i % abs(j), 0 ≤ i % abs(j), i0 < 0, i < 0 ⊦ j = 0, i % abs(j) = i0 |%| abs(j) ↔ i % j = i0 |%| j

Rule argument

spec: int-mod inst: name: mod-pos-def seq: ⊦ 0 ≤ i % j → i |%| j = i % j subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i