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Proof step 21 from proof modmod-add-law-pos (previous step)

j + (i0 % j + i % j) % j = (i + i0 % j) % j, (i0 % j + i % j) % j + 2 * j < j, 0 < j ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i + j = j + i
Proof step 23:
j + (i0 % j + i % j) % j = (i + i0 % j) % j, 2 * j + (i0 % j + i % j) % j < j, 0 < j ⊦ j = 0

Rule argument

spec: int-basic2 inst: name: add-c seq: ⊦ i + j = j + i subst: [j, i] → [2 * j, (i0 % j + i % j) % j] flags: rewrite

Additional information

Used terms: 2 * j, (i0 % j + i % j) % j