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Proof step 2 from proof mod-mult-neg-02 (previous step)

0 < j, i ≤ 0, i < j, i0 ≤ 0, i0 < j ⊦ (j * i + i0) % j = i0 % j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ i ≤ 0 ∧ i0 ≤ 0 ∧ abs(i0) < j → (j * i + i0) % j = i0
Proof step 4:
¬(0 < j ∧ i ≤ 0 ∧ i0 ≤ 0 ∧ abs(i0) < j), 0 < j, i ≤ 0, i < j, i0 ≤ 0, i0 < j ⊦ (j * i + i0) % j = i0 % j

Rule argument

spec: int-div inst: name: mod-mult-neg seq: ⊦ 0 < j ∧ i ≤ 0 ∧ i0 ≤ 0 ∧ abs(i0) < j → (j * i + i0) % j = i0 subst: [i0, i, j] → [i0, i, j] flags: rewrite, current

Additional information

Used simplifier rules: mod-zero-05: ⊦ abs(i) < j → i % j = i; Used terms: i0, i, j