Nuprl Lemma : geo-colinear-set_wf
∀[e:EuclideanPlaneStructure]. ∀[L:Point List]. (geo-colinear-set(e; L) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-colinear-set: geo-colinear-set(e; L),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-point: Point,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
geo-colinear-set: geo-colinear-set(e; L),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
list_wf,
geo-colinear_wf,
l_member_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
l_all_wf2
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
setEquality,
rename,
setElimination,
because_Cache,
lambdaFormation,
lambdaEquality,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlaneStructure]. \mforall{}[L:Point List]. (geo-colinear-set(e; L) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-04_39_56
Last ObjectModification:
2017_08_07-AM-11_04_31
Theory : euclidean!plane!geometry
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