Nuprl Lemma : not-eu-between-same2
∀e:EuclideanPlane. ∀[a,b:Point]. False supposing a-a-b
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between: a-b-c,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
false: False
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
prop: ℙ,
euclidean-plane: EuclideanPlane
Lemmas referenced :
euclidean-plane_wf,
eu-point_wf,
eu-between_wf,
not-eu-between-same,
eu-between-sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
voidElimination,
sqequalRule,
setElimination,
rename,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b:Point]. False supposing a-a-b
Date html generated:
2016_05_18-AM-06_34_19
Last ObjectModification:
2016_01_05-PM-00_57_02
Theory : euclidean!geometry
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