Nuprl Lemma : eu-between-eq-outer-trans

e:EuclideanPlane. ∀[a,b,c,d:Point].  (a_c_d) supposing (b_c_d and a_b_c and (b c ∈ Point)))


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 equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T not: ¬A implies:  Q false: False euclidean-plane: EuclideanPlane sq_stable: SqStable(P) prop: exists: x:A. B[x] and: P ∧ Q squash: T
Lemmas referenced :  eu-point_wf sq_stable__eu-between-eq eu-between-eq_wf eu-between-eq-same equal_wf eu-extend-exists not_wf euclidean-plane_wf eu-construction-unicity eu-between-eq-symmetry eu-between-eq-inner-trans eu-between-eq-exchange3 eu-congruent-symmetry
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction sqequalRule sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality voidElimination equalityEquality extract_by_obid isectElimination setElimination rename hypothesis because_Cache independent_functionElimination equalitySymmetry hyp_replacement Error :applyLambdaEquality,  independent_isectElimination dependent_set_memberEquality productElimination imageMemberEquality baseClosed imageElimination

\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d:Point].    (a\_c\_d)  supposing  (b\_c\_d  and  a\_b\_c  and  (\mneg{}(b  =  c)))

Date html generated: 2016_10_26-AM-07_41_13
Last ObjectModification: 2016_07_12-AM-08_07_23

Theory : euclidean!geometry

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