### Nuprl Lemma : eu-between-implies-between-eq

`∀e:EuclideanPlane. ∀[a,b,c:Point].  a_b_c supposing a-b-c`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-between: `a-b-c` eu-point: `Point` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` euclidean-plane: `EuclideanPlane` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` not: `¬A` false: `False` prop: `ℙ`
Lemmas referenced :  eu-between-eq-def and_wf not_wf equal_wf eu-point_wf eu-between_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename hypothesisEquality isectElimination hypothesis productElimination independent_functionElimination voidElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c:Point].    a\_b\_c  supposing  a-b-c

Date html generated: 2016_05_18-AM-06_33_54
Last ObjectModification: 2015_12_28-AM-09_27_50

Theory : euclidean!geometry

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