Nuprl Lemma : geo-parallel-points_wf
∀e:GeometryPrimitives. ∀a,b,c,d:Point.  (geo-parallel-points(e;a;b;c;d) ∈ ℙ)
Proof
Definitions occuring in Statement : 
geo-parallel-points: geo-parallel-points(e;a;b;c;d)
, 
geo-primitives: GeometryPrimitives
, 
geo-point: Point
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
geo-parallel-points: geo-parallel-points(e;a;b;c;d)
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
not_wf, 
geo-intersect-points_wf, 
geo-point_wf, 
geo-primitives_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
sqequalRule, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_functionElimination, 
hypothesisEquality, 
hypothesis, 
inhabitedIsType, 
universeIsType
Latex:
\mforall{}e:GeometryPrimitives.  \mforall{}a,b,c,d:Point.    (geo-parallel-points(e;a;b;c;d)  \mmember{}  \mBbbP{})
Date html generated:
2019_10_16-PM-01_46_01
Last ObjectModification:
2019_06_19-PM-01_45_33
Theory : euclidean!plane!geometry
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