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Proof step 20 from proof less-mult-div-01 (previous step)

0 < (i1 * (i0 * j + j0)) / j, j0 < j, i1 < j, 0 < j1, 0 < j, 0 < i0 * j + j0, 0 ≤ j0, 0 ≤ i0, i0 * j + j0 ≤ (i1 * (i0 * j + j0)) / j, 0 ≤ i0 * j + j0, 0 ≤ (i1 * (i0 * j + j0)) / j ⊦ j0 = 0, 0 ≤ i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ i ≤ j ↔ ¬ j < i
Proof step 22:
i1 < 0, 0 < i0 * j + j0, 0 < j, 0 < j1, i1 < j, j0 < j, 0 < (i1 * (i0 * j + j0)) / j, 0 ≤ (i1 * (i0 * j + j0)) / j, 0 ≤ i0 * j + j0, i0 * j + j0 ≤ (i1 * (i0 * j + j0)) / j, 0 ≤ i0, 0 ≤ j0 ⊦ j0 = 0

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [i1, 0] flags: <all paths>

Additional information

Used terms: i1, 0