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Theorem div-elim2

⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: div-add-neg, div-elim-negpos, div-lezero, div-zero-01, div2-add-neg, div2-neg-01, div2-notzero, div2-zero, diveq-neg, exeven, mod-add-neg, mod-grz, mod-lsz, mod-zero-05, mod2-add-neg, mod2-neg-odd, modeq-neg, modeq-neg-02, modeq-pos-03, modeven-neg, modeven-neg-01, modex, mult-ls, mult-ls-01, nummult-le-01, nummult-le-03, nummult-ls-01, nummult-ls-03, one, zero-04,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: divmod-rew, mod-neg-01, neg-01, div-elim,
Used spec theorems:
- Used simplifier rules: