Nuprl Lemma : eu-colinear-set_wf
∀[e:EuclideanPlane]. ∀[L:Point List]. (eu-colinear-set(e;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-colinear-set: eu-colinear-set(e;L),
euclidean-plane: EuclideanPlane,
eu-point: Point,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
euclidean-plane: EuclideanPlane,
eu-colinear-set: eu-colinear-set(e;L),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
l_all_wf2,
eu-point_wf,
l_member_wf,
not_wf,
equal_wf,
eu-colinear_wf,
list_wf,
euclidean-plane_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
setEquality,
functionEquality,
because_Cache,
lambdaFormation,
lambdaEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[L:Point List]. (eu-colinear-set(e;L) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_40_18
Last ObjectModification:
2016_01_03-PM-01_52_08
Theory : euclidean!geometry
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