Nuprl Lemma : coprime_bezout_id0
∀a,b:ℤ. (CoPrime(a,b) ⇒ (∃x,y:ℤ. (((a * x) + (b * y)) ~ 1)))
Proof
Definitions occuring in Statement :
coprime: CoPrime(a,b),
assoced: a ~ b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
prop: ℙ,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
coprime: CoPrime(a,b),
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
istype-int,
coprime_wf,
bezout_ident,
gcd_p_sym,
gcd_unique,
assoced_wf,
mul-commutes,
istype-void,
add-commutes
Rules used in proof :
Error :inhabitedIsType,
hypothesis,
isectElimination,
Error :universeIsType,
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
sqequalHypSubstitution,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
natural_numberEquality,
multiplyEquality,
addEquality,
Error :productIsType,
sqequalRule,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}a,b:\mBbbZ{}. (CoPrime(a,b) {}\mRightarrow{} (\mexists{}x,y:\mBbbZ{}. (((a * x) + (b * y)) \msim{} 1)))
Date html generated:
2019_06_20-PM-02_23_34
Last ObjectModification:
2019_01_15-PM-01_48_41
Theory : num_thy_1
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