### Nuprl Lemma : eu-seg-length-test

`∀e:EuclideanPlane. ∀[a,b,c,d,x,y:Point].  (ba=xy) supposing (dc=yx and ab=cd)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` 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` uiff: `uiff(P;Q)` and: `P ∧ Q` prop: `ℙ` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  euclidean-plane_wf eu-point_wf eu-congruent_wf eu-length-flip eu-congruent-iff-length
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality isectElimination productElimination independent_isectElimination because_Cache hypothesis equalityTransitivity equalitySymmetry setElimination rename

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,d,x,y:Point].    (ba=xy)  supposing  (dc=yx  and  ab=cd)

Date html generated: 2016_05_18-AM-06_41_17
Last ObjectModification: 2016_01_04-PM-02_45_44

Theory : euclidean!geometry

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