Nuprl Lemma : gcd_unique
∀a,b,y1,y2:ℤ. (GCD(a;b;y1) ⇒ GCD(a;b;y2) ⇒ (y1 ~ y2))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
assoced: a ~ b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
assoced: 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 :
divides_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
independent_pairFormation,
cut,
hypothesis,
sqequalHypSubstitution,
productElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
Error :productIsType,
Error :universeIsType,
introduction,
extract_by_obid,
isectElimination,
Error :functionIsType,
Error :inhabitedIsType
Latex:
\mforall{}a,b,y1,y2:\mBbbZ{}. (GCD(a;b;y1) {}\mRightarrow{} GCD(a;b;y2) {}\mRightarrow{} (y1 \msim{} y2))
Date html generated:
2019_06_20-PM-02_21_48
Last ObjectModification:
2018_10_03-AM-00_12_06
Theory : num_thy_1
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