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Proof step 1 from proof modmod-add-law (conclusion)

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

User applied rule cut formula

And obtained the following new goals

Proof step 2:
j < 0, 0 ≠ j ⊦ (i % j + i0 % j) % j = (i + i0) % j ∨ (i % j + i0 % j) % j = (i + i0) % j + j ∨ (i % j + i0 % j) % j = (i + i0) % j - j
Proof step 4:
0 ≠ j ⊦ j < 0, (i % j + i0 % j) % j = (i + i0) % j ∨ (i % j + i0 % j) % j = (i + i0) % j + j ∨ (i % j + i0 % j) % j = (i + i0) % j - j

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0