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

⊦ (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, 0 = j

User applied rule cut formula

And obtained the following new goals

Proof step 3:
j < 0 ⊦ (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, 0 = j
Proof step 5:
⊦ (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, 0 = j, j < 0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0