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Proof step 4 from proof mod-zero-06 (previous step)

j ≠ 0, 0 ≤ i, i - i / j * j < 0, 0 < i, (i - i / j * j) + 1 < i, abs(j) = 1 ∨ abs(j) ≤ i ⊦ j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ i, i < i / j * j, 0 < i, 1 < i / j * j, 0 < i / j * j, abs(j) = 1 ∨ abs(j) ≤ i ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs