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Proof step 67 from proof congmod-def-mod-02 (previous step)

i < 0, i0 < 0, i % j < 0, i0 % j < 0 ⊦ i % j = i0 % j ↔ i % j + 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-neg-def seq: ⊦ i % j < 0 → i |%| j = i % j + j subst: [j, i] → [j, i0] flags: rewrite, current

Additional information

Used simplifier rules: add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, i0