### 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))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-colinear: `Colinear(a;b;c)` eu-congruent: `ab=cd` eu-point: `Point` uimplies: `b 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: `b supposing a` member: `t ∈ T` prop: `ℙ` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` 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

Latex:
\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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