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Proof step 4 from proof mod-zero-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
1 + i < i / j * j + j, 0 < j, 0 ≤ i, i < i / j * j, 0 < i / j ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%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