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Proof step 7 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 ⊦ i * i1 + 0 = i0 * j + j0 ∧ 0 ≤ 0 ∧ i1 ≤ j ∧ 0 ≤ i ∧ i < i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i + 0 = i
Proof step 9:
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 = i0 * j + j0 ∧ 0 ≤ 0 ∧ i1 ≤ j ∧ 0 ≤ i ∧ i < i0

Rule argument

spec: int-basic2 inst: name: add-zero seq: ⊦ i + 0 = i subst: [i] → [i * i1] flags: rewrite

Additional information

Used terms: i * i1