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Proof step 8 from proof less-mult-div-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i * j * j0 = (i * j) * j0
Proof step 10:
j0 < j, i1 < j, 0 < j1, 0 < j, 0 < i0 * j + j0, 0 < (i0 * j * i1 + j0 * i1) / j, 0 ≤ j0, 0 ≤ i0, i0 * j + j0 ≤ (i0 * j * i1 + j0 * i1) / j, 0 ≤ i0 * j + j0, 0 ≤ (i0 * j * i1 + j0 * i1) / j ⊦

Rule argument

spec: int-mult name: associativity seq: ⊦ i * j * j0 = (i * j) * j0 subst: [j0, j, i] → [i1, j, i0] flags: <rotated> <all paths>

Additional information

Used terms: i1, j, i0