Nuprl Lemma : eu-colinear-between

  ∀[A,B,C,D:Point].  (Colinear(A;C;D)) supposing ((¬(A C ∈ Point)) and (A B ∈ Point)) and A_C_B and A_D_B)


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-colinear: Colinear(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) squash: T prop: and: P ∧ Q exists: x:A. B[x]
Lemmas referenced :  eu-point_wf sq_stable__colinear not_wf equal_wf eu-between-eq_wf euclidean-plane_wf eu-proper-extend-exists eu-O_wf eu-not-colinear-OXY eu-X_wf eu-colinear-same-side eu-between-eq-symmetry eu-between-implies-between-eq eu-between-eq-exchange3 eu-between-eq-exchange4 eu-between_wf not-eu-between-same
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 imageMemberEquality baseClosed imageElimination equalitySymmetry dependent_set_memberEquality productElimination independent_isectElimination hyp_replacement Error :applyLambdaEquality

    \mforall{}[A,B,C,D:Point].    (Colinear(A;C;D))  supposing  ((\mneg{}(A  =  C))  and  (\mneg{}(A  =  B))  and  A\_C\_B  and  A\_D\_B)

Date html generated: 2016_10_26-AM-07_43_18
Last ObjectModification: 2016_07_12-AM-08_09_10

Theory : euclidean!geometry

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