Nuprl Lemma : coprime_intro
∀a,b:ℤ. ((∀c:ℤ. ((c | a) ⇒ (c | b) ⇒ (c | 1))) ⇒ CoPrime(a,b))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
coprime: CoPrime(a,b),
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
one_divs_any,
divides_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,
hypothesis,
independent_functionElimination,
productElimination,
Error :productIsType,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType,
Error :functionIsType,
natural_numberEquality
Latex:
\mforall{}a,b:\mBbbZ{}. ((\mforall{}c:\mBbbZ{}. ((c | a) {}\mRightarrow{} (c | b) {}\mRightarrow{} (c | 1))) {}\mRightarrow{} CoPrime(a,b))
Date html generated:
2019_06_20-PM-02_23_22
Last ObjectModification:
2018_10_03-AM-00_12_33
Theory : num_thy_1
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