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Proof step 17 from proof modmod-add-if (previous step)

0 < j, i < 0, 0 ≤ i0 ⊦ (i + i0 % j) % j = (0 ≤ i + i0 % j ⊃ (i + i0) % j;((i + i0 % j) % j ≠ 0 ⊃ (i + i0) % j - j;0)), i + i0 < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
0 < j, i < 0, 0 ≤ i + i0, 0 ≤ i0 ⊦ (i + i0 % j) % j = (0 ≤ i + i0 % j ⊃ (i + i0) % j;((i + i0 % j) % j ≠ 0 ⊃ (i + i0) % j - j;0))

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)