Nuprl Lemma : geo-seg1_wf
∀[e:EuclideanPlaneStructure]. ∀[s:geo-segment(e)]. (geo-seg1(s) ∈ Point)
Proof
Definitions occuring in Statement :
geo-seg1: geo-seg1(s),
geo-segment: geo-segment(e),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
geo-segment: geo-segment(e),
subtype_rel: A ⊆r B,
geo-seg1: geo-seg1(s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
geo-segment_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
pi1_wf_top
Rules used in proof :
because_Cache,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
voidEquality,
voidElimination,
isect_memberEquality,
independent_pairEquality,
productElimination,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlaneStructure]. \mforall{}[s:geo-segment(e)]. (geo-seg1(s) \mmember{} Point)
Date html generated:
2017_10_02-PM-04_44_12
Last ObjectModification:
2017_08_05-AM-09_25_33
Theory : euclidean!plane!geometry
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