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Proof step 10 from proof less-mult-div-01 (previous step)

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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i * j = j * i
Proof step 12:
0 < (i0 * i1 * j + j0 * i1) / j, 0 < i0 * j + j0, 0 < j, 0 < j1, i1 < j, j0 < j, 0 ≤ (i0 * i1 * j + j0 * i1) / j, 0 ≤ i0 * j + j0, i0 * j + j0 ≤ (i0 * i1 * j + j0 * i1) / j, 0 ≤ i0, 0 ≤ j0 ⊦

Rule argument

spec: int-mult name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [i1, j] flags: <all paths>

Additional information

Used terms: i1, j