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Proof step 2 from proof modmod-add-case (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, j, i0