### Nuprl Lemma : eu-congruent-transitivity

`∀e:EuclideanPlane. ∀[a,b,c,d,x,y:Point].  (ab=xy) supposing (cd=xy 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` prop: `ℙ` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` euclidean-axioms: `euclidean-axioms(e)` and: `P ∧ Q` squash: `↓T` guard: `{T}`
Lemmas referenced :  eu-congruent-refl sq_stable__eu-congruent euclidean-plane_wf eu-point_wf eu-congruent_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut hypothesisEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesis dependent_functionElimination independent_functionElimination introduction productElimination sqequalRule imageMemberEquality baseClosed imageElimination equalityTransitivity equalitySymmetry independent_isectElimination

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

Date html generated: 2016_05_18-AM-06_34_53
Last ObjectModification: 2016_01_16-PM-10_31_02

Theory : euclidean!geometry

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