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: supposing a uall: [x:A]. B[x] all: x:A. B[x] not: ¬A and: P ∧ Q equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] member: t ∈ T uall: [x:A]. B[x] uimplies: supposing a not: ¬A implies:  Q and: P ∧ Q false: False prop: 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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