Nuprl Lemma : geo-mk-seg_wf
∀[e:EuclideanPlaneStructure]. ∀[a,b:Point]. (ab ∈ geo-segment(e))
Proof
Definitions occuring in Statement :
geo-mk-seg: ab,
geo-segment: geo-segment(e),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
geo-segment: geo-segment(e),
subtype_rel: A ⊆r B,
geo-mk-seg: ab,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
euclidean-plane-structure-subtype,
geo-point_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
thin,
isectElimination,
extract_by_obid,
productEquality,
sqequalHypSubstitution,
lambdaEquality,
applyEquality,
hypothesis,
hypothesisEquality,
independent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlaneStructure]. \mforall{}[a,b:Point]. (ab \mmember{} geo-segment(e))
Date html generated:
2017_10_02-PM-04_44_07
Last ObjectModification:
2017_08_05-AM-09_25_07
Theory : euclidean!plane!geometry
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