Nuprl Lemma : gcd_p_wf
∀[a,b,y:ℤ].  (GCD(a;b;y) ∈ ℙ)
Proof
Definitions occuring in Statement : 
gcd_p: GCD(a;b;y)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
gcd_p: GCD(a;b;y)
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
Lemmas referenced : 
divides_wf, 
all_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
intEquality, 
lambdaEquality, 
functionEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
isect_memberEquality, 
because_Cache, 
Error :universeIsType
Latex:
\mforall{}[a,b,y:\mBbbZ{}].    (GCD(a;b;y)  \mmember{}  \mBbbP{})
Date html generated:
2019_06_20-PM-02_21_20
Last ObjectModification:
2018_09_26-PM-05_49_04
Theory : num_thy_1
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