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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