### Nuprl Lemma : eu-between-eq-same-side2

`∀e:EuclideanPlane. ∀[A,B,C,D:Point].  (¬((¬B_C_D) ∧ (¬B_D_C))) supposing ((¬(A = B ∈ Point)) and A_B_C and A_B_D)`

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]` all: `∀x:A. B[x]` not: `¬A` and: `P ∧ Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` and: `P ∧ Q` false: `False` prop: `ℙ` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  eu-between-eq-same-side eu-between-eq-symmetry eu-between-eq-inner-trans eu-between-eq-exchange3 eu-between-eq_wf and_wf not_wf equal_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality isect_memberFormation isectElimination introduction independent_isectElimination independent_functionElimination independent_pairFormation productElimination promote_hyp because_Cache voidElimination setElimination rename sqequalRule lambdaEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}e:EuclideanPlane
\mforall{}[A,B,C,D:Point].    (\mneg{}((\mneg{}B\_C\_D)  \mwedge{}  (\mneg{}B\_D\_C)))  supposing  ((\mneg{}(A  =  B))  and  A\_B\_C  and  A\_B\_D)

Date html generated: 2016_05_18-AM-06_39_50
Last ObjectModification: 2015_12_28-AM-09_23_35

Theory : euclidean!geometry

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