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Proof step 17 from proof modmod-add-case (
previous step
)
⊦ i + i0 % j < 0 ∧ 0 ≤ i + i0 ∧ i < 0 ∧ 0 ≤ i0 ∧ (i + i0 % j) % j ≠ 0 ∧ 0 < j → (i + i0 % j) % j = (i + i0) % j - j
Lemma
modmod-add2-negpos-pos-01