Nuprl Lemma : geo-seg-of_wf
∀[e:BasicGeometry]. ∀[sp:geo-proper-segment(e)]. (geo-seg-of(sp) ∈ geo-segment(e))
Proof
Definitions occuring in Statement :
geo-seg-of: geo-seg-of(sp),
geo-proper-segment: geo-proper-segment(e),
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
geo-proper-segment: geo-proper-segment(e),
euclidean-plane: EuclideanPlane,
basic-geometry: BasicGeometry,
geo-seg-of: geo-seg-of(sp),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
basic-geometry_wf,
geo-proper-segment_wf,
geo-segment_wf,
pi1_wf_top
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
voidEquality,
voidElimination,
isect_memberEquality,
hypothesisEquality,
independent_pairEquality,
productElimination,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[sp:geo-proper-segment(e)]. (geo-seg-of(sp) \mmember{} geo-segment(e))
Date html generated:
2017_10_02-PM-04_44_43
Last ObjectModification:
2017_08_08-PM-01_04_02
Theory : euclidean!plane!geometry
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