### Nuprl Lemma : eu-be-compress

`∀e:EuclideanPlane. ∀a,b,c:Point.  (a_b_c `` a_c_b `` (b = c ∈ Point))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-point: `Point` all: `∀x:A. B[x]` implies: `P `` Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` uimplies: `b supposing a`
Lemmas referenced :  eu-between-eq_wf eu-point_wf euclidean-plane_wf eu-between-eq-exchange3 eu-between-eq-same
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut hypothesis lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality dependent_functionElimination because_Cache independent_isectElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    (a\_b\_c  {}\mRightarrow{}  a\_c\_b  {}\mRightarrow{}  (b  =  c))

Date html generated: 2016_05_18-AM-06_45_25
Last ObjectModification: 2015_12_28-AM-09_21_49

Theory : euclidean!geometry

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