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Proof step 2 from proof one-neg (previous step)

1 / j < 0 ⊦ j = 0, j = ~1

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:
1 / j < 0 ⊦ 0 < j ∧ 0 < 1, j = 0, j = ~1
Proof step 14:
1 = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 < j ∧ 0 < 1, i0 < 0 ⊦ j = 0, j = ~1

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] → [1, j, i, j0] flags: rewrite, current

Additional information

Used terms: 1, j, i, j0