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Proof step 4 from proof mod-ls-same (previous step)

j ≠ 0, 0 < j, 0 ≤ i, j ≤ i - i / j * j, 0 < i - i / j * j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: add-zero: ⊦ i + 0 = i; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; 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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%succ-rmerge: ⊦ i * j + i = i * (j + 1); from specification int-mult%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs