Nuprl Lemma : eu-colinear-equidistant

e:EuclideanPlane. ∀[a,b,c,p,q:Point].  (cp=cq) supposing (ap=aq and bp=bq and Colinear(a;b;c))


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-colinear: Colinear(a;b;c) eu-congruent: ab=cd eu-point: Point uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x]
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T prop: euclidean-plane: EuclideanPlane sq_stable: SqStable(P) implies:  Q squash: T
Lemmas referenced :  eu-colinear-five-segment sq_stable__eu-congruent eu-congruent-refl euclidean-plane_wf eu-point_wf eu-colinear_wf eu-congruent_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache dependent_functionElimination independent_functionElimination introduction sqequalRule imageMemberEquality baseClosed imageElimination independent_isectElimination

\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,p,q:Point].    (cp=cq)  supposing  (ap=aq  and  bp=bq  and  Colinear(a;b;c))

Date html generated: 2016_05_18-AM-06_39_15
Last ObjectModification: 2016_01_16-PM-10_29_09

Theory : euclidean!geometry

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