Nuprl Lemma : coprime_elim_a
∀a,b:ℤ. (CoPrime(a,b) ⇐⇒ gcd(a;b) ~ 1)
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
assoced: a ~ b,
gcd: gcd(a;b),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
coprime: CoPrime(a,b),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
istype-int,
gcd_wf,
gcd_sat_pred,
gcd_p_wf,
assoced_wf,
gcd_unique,
gcd_p_functionality_wrt_assoced,
assoced_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
isectElimination,
independent_pairFormation,
Error :universeIsType,
natural_numberEquality,
Error :equalityIsType1,
equalityTransitivity,
independent_functionElimination,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}a,b:\mBbbZ{}. (CoPrime(a,b) \mLeftarrow{}{}\mRightarrow{} gcd(a;b) \msim{} 1)
Date html generated:
2019_06_20-PM-02_23_27
Last ObjectModification:
2018_10_03-AM-00_12_39
Theory : num_thy_1
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