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Theorem div-elim

n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: div-mult, div-succ, div-succ-01, le-div-to-mult, le-succ, ls, ls-01, mod-eq-01, mod-ls-01, mod-ls-02, mod-ls-03, mod-rew, mod-succ, mod-succ-01, mod-succ-04, mod2-succ, modex, square-even, square-nle-01, square-nls, two-eq, two-loup, two-loup-02, two-loup-04, two-loup-05, two-loup-06, two-loup-07, two-loup-08, two-loup-09, two-loup-10, two-loup-11, two-loup-12, two-loup-13, two-ls, two-ls-02, two-mdiv2-02, two-neq, two-neq-01, two-neq-02, two-odd-01, two-peq, two-ppred, two-zero-01-01,
Used by units in proved state: nat-prime, nat-pot, nat-even, intnat, int-pair,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: zero-01, mult, mod-ls, Moddef,
Used spec theorems:
- Used simplifier rules: