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Proof step 5 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, 0 ≤ i0 ∧ 0 ≤ i

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i < 0, 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, 0 ≤ i0 ∧ 0 ≤ i
Proof step 18:
0 < j ⊦ i < 0, (i + i0 % j) % j = (i + i0) % j, (i + i0 % j) % j = (i + i0) % j + j, (i + i0) % j = (i + i0 % j) % j + j, 0 ≤ i0 ∧ 0 ≤ i

Rule argument

fma: i < 0

Additional information

Used formulas: i < 0