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

`∀[e:EuclideanPlane]. ∀[a,b:Point].  a = b ∈ Point supposing a_b_a`

Proof

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

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a,b:Point].    a  =  b  supposing  a\_b\_a

Date html generated: 2016_05_18-AM-06_34_22
Last ObjectModification: 2015_12_28-AM-09_27_40

Theory : euclidean!geometry

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