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Proof step 8 from proof modmod-add-zero (previous step)

(i + i0 % j) % j = 0, 0 < j ⊦ (i + i0) % j = 0, 0 = j, 0 ≤ i0 ∧ 0 ≤ i, i ≤ 0 ∧ i0 ≤ 0

User applied rule cut formula

And obtained the following new goals

Proof step 9:
i0 < 0, (i + i0 % j) % j = 0, 0 < j ⊦ (i + i0) % j = 0, 0 = j, 0 ≤ i0 ∧ 0 ≤ i, i ≤ 0 ∧ i0 ≤ 0
Proof step 17:
(i + i0 % j) % j = 0, 0 < j ⊦ i0 < 0, (i + i0) % j = 0, 0 = j, 0 ≤ i0 ∧ 0 ≤ i, i ≤ 0 ∧ i0 ≤ 0

Rule argument

fma: i0 < 0

Additional information

Used formulas: i0 < 0