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Proof step 2 from proof div-mod-eq (previous step)

⊦ j = 0, i |/| j * j + i |%| j = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i % j → i |%| j = i % j
Proof step 4:
¬ 0 ≤ i % j ⊦ j = 0, i |/| j * j + i |%| j = i
Proof step 12:
0 ≤ i % j ⊦ j = 0, i |/| j * j + i % j = i

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