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Theorem div-elim-pos

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: div-add-pos, div-div-pos, div-elim, div-elim-pospos, div-elim1, div-mult-02, div-rec, div-two-zero-01, div-twoodd, div-zero, div2-add-neg, exeven, exodd, leone-two, ls, ls-01, ls-02, mod-add-pos, mod-les, mod-nls-01, mod-pred-02, mod-rec, mod-twoodd-02, mod-zero-03, mod2-add-neg, modeq-neg-02, modeq-pos-02, modeven-pos, modex, modmod-add, modmod-mult, modmod-mult-04, mult-02, mult-ls, mult-ls-01, num-ls, nummult-le, nummult-le-01, nummult-le-02, nummult-ls, one, zero-04,
Used by units in proved state: int-pot, intnat,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: modeq-pos, diveq-pos, mod-ls-same, mod-zero, divmod-rew,
Used spec theorems:
- Used simplifier rules: