Nuprl Lemma : coprime_inversion
∀a,b:ℤ. (CoPrime(a,b) ⇐⇒ CoPrime(b,a))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ
Definitions unfolded in proof :
coprime: CoPrime(a,b),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
gcd_p_sym,
gcd_p_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
independent_functionElimination,
hypothesis,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType
Latex:
\mforall{}a,b:\mBbbZ{}. (CoPrime(a,b) \mLeftarrow{}{}\mRightarrow{} CoPrime(b,a))
Date html generated:
2019_06_20-PM-02_22_37
Last ObjectModification:
2018_10_03-AM-00_12_28
Theory : num_thy_1
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