Nuprl Lemma : coprime-mod
∀n:ℕ+. ∀x:ℤ. (CoPrime(n,x) ⇐⇒ CoPrime(n,x mod n))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
modulus: a mod n,
nat_plus: ℕ+,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
mod-eqmod,
nat_plus_wf,
coprime_wf,
coprime_functionality_wrt_eqmod2,
modulus_wf_int_mod,
int-subtype-int_mod,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
independent_pairFormation,
isectElimination,
setElimination,
rename,
because_Cache,
addLevel,
productElimination,
impliesFunctionality,
applyEquality,
sqequalRule,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}x:\mBbbZ{}. (CoPrime(n,x) \mLeftarrow{}{}\mRightarrow{} CoPrime(n,x mod n))
Date html generated:
2018_05_21-PM-01_09_50
Last ObjectModification:
2018_01_28-PM-02_03_36
Theory : num_thy_1
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