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Proof step 8 from proof nummult-ls-03 (previous step)

j + 1 = i2 + i1, j < 0, i1 ≤ j, i1 < 0 ⊦ j < i2 * i0 ↔ i1 / i2 < i0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)
Proof step 10:
j + 1 = i2 + i1, j < 0, i1 ≤ j, i1 < 0 ⊦ 0 < i2 ∧ i1 < 0, j < i2 * i0 ↔ i1 / i2 < i0
Proof step 13:
i1 = i3 * i2 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < i2 ∧ 0 < i2, j + 1 = i2 + i1, j < 0, i1 ≤ j, i1 < 0 ⊦ j < i2 * i0 ↔ i3 < i0

Rule argument

spec: int-div inst: name: div-elim2 seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j) subst: [i, j, i0, j0] → [i1, i2, i, j0] flags: current, []

Additional information

Used terms: i1, i2, i, j0