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

0 < j, i0 < j, 0 ≤ i0, 0 ≤ i ⊦ i0 % j = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ abs(i) < j → i % j = i

Rule argument

spec: <toplevel> name: mod-zero-05 seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [j, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 ≤ i → abs(i) = i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: j, i0