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Proof step 12 from proof congmod-def-mod-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%mod-zero-06: ⊦ 0 ≤ i ∧ j ≠ 0 → ¬ i % j < 0; from specification int-div Used terms: j, i