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Proof step 2 from proof less-mult-div-01 (previous step)

i1 < j, i ≤ (i * i1) / j, 0 < i, 0 < j, 0 < j1, 0 < (i * i1) / j ⊦

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ 0 < i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)
Proof step 4:
i1 < j, i ≤ (i * i1) / j, 0 < i, 0 < j, 0 < j1, 0 < (i * i1) / j ⊦ 0 < j ∧ 0 < i * i1
Proof step 7:
i * i1 = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 < i * i1, i1 < j, i ≤ i0, 0 < i, 0 < j, 0 < j1, 0 < i0 ⊦

Rule argument

spec: int-div inst: name: div-elim seq: ⊦ 0 < j ∧ 0 < i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i * i1, j, i0, j0] flags: current, []

Additional information

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