Nuprl Lemma : geo-length_wf
∀[e:BasicGeometry]. ∀[s:geo-segment(e)]. (|s| ∈ Length)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-segment: geo-segment(e),
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
basic-geometry_wf,
geo-segment_wf,
subtype-geo-length-type,
geo-length_wf1
Rules used in proof :
because_Cache,
isect_memberEquality,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[s:geo-segment(e)]. (|s| \mmember{} Length)
Date html generated:
2017_10_02-PM-04_51_49
Last ObjectModification:
2017_08_05-AM-09_09_58
Theory : euclidean!plane!geometry
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