Nuprl Lemma : coprime_functionality_wrt_eqmod2
∀a,a',m:ℤ. ((a' ≡ a mod m) ⇒ (CoPrime(m,a') ⇐⇒ CoPrime(m,a)))
Proof
Definitions occuring in Statement :
eqmod: a ≡ b mod m,
coprime: CoPrime(a,b),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
coprime_inversion,
coprime_wf,
iff_wf,
eqmod_wf,
coprime_functionality_wrt_eqmod
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
addLevel,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
impliesFunctionality,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
isectElimination,
intEquality
Latex:
\mforall{}a,a',m:\mBbbZ{}. ((a' \mequiv{} a mod m) {}\mRightarrow{} (CoPrime(m,a') \mLeftarrow{}{}\mRightarrow{} CoPrime(m,a)))
Date html generated:
2016_05_14-PM-04_22_41
Last ObjectModification:
2015_12_26-PM-08_18_34
Theory : num_thy_1
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