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Proof step 5 from proof prod-div-less (previous step)

i * i1 = i0 * j + j0, i < j, i1 < j, i ≤ i0, 0 < i, 0 < i1, 0 < j, 1 < j, j0 < j, 0 < i0, 0 ≤ j0, 0 ≤ i0, 0 ≤ i1 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 6:
i * i0 + j0 = i1 * j + j1, 0 ≤ j1, j1 < j, 0 ≤ j0, j0 < j, 0 ≤ i0, i0 ≤ j, 0 ≤ i, i < i1 ⊦
Proof step 7:
i * i1 = i0 * j + j0, i < j, i1 < j, i ≤ i0, 0 < i, 0 < i1, 0 < j, 1 < j, j0 < j, 0 < i0, 0 ≤ j0, 0 ≤ i0, 0 ≤ i1 ⊦ i * i1 + 0 = i0 * j + j0 ∧ 0 ≤ 0 ∧ i1 ≤ j ∧ 0 ≤ i ∧ i < i0

Rule argument

spec: int-mult inst: name: modneqp seq: i * i0 + j0 = i1 * j + j1, 0 ≤ j1, j1 < j, 0 ≤ j0, j0 < j, 0 ≤ i0, i0 ≤ j, 0 ≤ i, i < i1 ⊦ subst: [i, i0, j0, i1, j, j1] → [i, i1, 0, i0, j, j0] flags:

Additional information

Used terms: i, i1, 0, i0, j, j0