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Proof step 7 from proof modmod-add-law-pos (previous step)

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

User applied rule insert equation

And obtained the following new goals

Proof step 8:
(i0 % j + i % j) % j = (i0 % j + i) % j + j, 0 < j, (i + i0 % j) % j = (i + i0) % j ∨ (i + i0 % j) % j = (i + i0) % j + j ∨ (i + i0 % j) % j = (i + i0) % j - j ⊦ (i0 % j + i) % j + j = (i + i0) % j, (i0 % j + i) % j + j = (i + i0) % j + j, (i0 % j + i) % j + j = (i + i0) % j - j

Rule argument

pos: left 1 flags:

Additional information

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