### Nuprl Lemma : residue-mul_wf

`∀[n:ℕ+]. ∀[a,i:ℤ].  (ai mod n) ∈ residue(n) supposing CoPrime(n,a) ∧ CoPrime(n,i)`

Proof

Definitions occuring in Statement :  residue-mul: `(ai mod n)` residue: `residue(n)` coprime: `CoPrime(a,b)` nat_plus: `ℕ+` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` and: `P ∧ Q` member: `t ∈ T` int: `ℤ`
Definitions unfolded in proof :  residue: `residue(n)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` residue-mul: `(ai mod n)` and: `P ∧ Q` int_seg: `{i..j-}` subtype_rel: `A ⊆r B` lelt: `i ≤ j < k` nat_plus: `ℕ+` prop: `ℙ` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` implies: `P `` Q`
Lemmas referenced :  modulus_wf_int_mod mod_bounds_1 mod_bounds lelt_wf coprime-mod coprime_wf and_wf nat_plus_wf coprime_prod
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin dependent_set_memberEquality lemma_by_obid isectElimination hypothesisEquality multiplyEquality hypothesis applyEquality because_Cache independent_pairFormation natural_numberEquality setElimination rename dependent_functionElimination independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality intEquality

Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  \mforall{}[a,i:\mBbbZ{}].    (ai  mod  n)  \mmember{}  residue(n)  supposing  CoPrime(n,a)  \mwedge{}  CoPrime(n,i)

Date html generated: 2016_05_15-PM-07_29_35
Last ObjectModification: 2015_12_27-AM-11_20_07

Theory : general

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