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Proof step 8 from proof mod-abs-pos (previous step)

j < 0, 0 ≤ i ⊦ i |%| ~ j = i |%| 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: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j; from specification int-div%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