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Proof step 17 from proof mod-div-ls (previous step)

0 < (i0 + i1 * j0) / j, i0 < (i0 + i1 * j0) / j, i0 < i1, 0 < j, 0 < i1, j0 < j, i1 ≤ (i1 * (j0 + 1)) / j, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, 0 ≤ j0, 0 ≤ i2 ⊦ j0 + 1 = j, (i1 * (j0 + 1)) / j < i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: less-mult-div-02 seq: ⊦ 0 < i ∧ 0 < j ∧ i1 < j → (i * i1) / j < i subst: [j, i1, i] → [j, j0 + 1, i1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, j0 + 1, i1