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Proof step 3 from proof mod-zero-06 (previous step)

i % j < 0, 0 < i, 0 ≤ i, abs(j) = 1 ∨ abs(j) ≤ i ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
j ≠ 0 ⊦ i % j = i - i / j * j
Proof step 5:
0 < i, i - i / j * j < 0, 0 ≤ i, abs(j) = 1 ∨ abs(j) ≤ i ⊦ j = 0

Rule argument

spec: <toplevel> name: mod-rew seq: j ≠ 0 ⊦ i % j = i - i / j * j subst: [j, i] → [j, i] flags: <all paths>

Additional information

Used terms: j, i