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Proof step 5 from proof mod-ls-same (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < j, i / j * j < i, 0 ≤ i, j * (i / j + 1) ≤ i ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + 0 = i; (s)% ⊦ i < j - i0 ↔ i + i0 < j; (s)%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% ⊦ i * j + i = i * (j + 1); (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)