Nuprl Lemma : geo-lt-pt_wf
∀[e:EuclideanPlaneStructure]. ∀[a,b,c,d:Point]. (ab < cd ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-lt-pt: ab < cd,
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
geo-lt-pt: ab < cd,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
euclidean-plane-structure-subtype,
geo-congruent_wf,
geo-strict-between_wf,
geo-point_wf,
exists_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
lambdaEquality,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlaneStructure]. \mforall{}[a,b,c,d:Point]. (ab < cd \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_36_14
Last ObjectModification:
2017_08_08-PM-00_35_03
Theory : euclidean!plane!geometry
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