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Proof step 19 from proof mod-div-ls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ j0 ≤ i / j ∧ i ≤ i0 ∧ 0 < j → j0 ≤ i0 / j

Rule argument

spec: <toplevel> name: div-le-pos seq: ⊦ j0 ≤ i / j ∧ i ≤ i0 ∧ 0 < j → j0 ≤ i0 / j subst: [j0, i, j, i0] → [i1, i0 + i1 * j0, j, i1 + i1 * j0] flags: <all paths>

Additional information

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