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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