### Nuprl Lemma : eu-seg-congruent_transitivity

`∀e:EuclideanPlane. ∀[s1,s2,s3:Segment].  (s1 ≡ s3) supposing (s1 ≡ s2 and s2 ≡ s3)`

Proof

Definitions occuring in Statement :  eu-seg-congruent: `s1 ≡ s2` eu-segment: `Segment` euclidean-plane: `EuclideanPlane` 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` eu-seg-congruent: `s1 ≡ s2` member: `t ∈ T` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` squash: `↓T` prop: `ℙ`
Lemmas referenced :  euclidean-plane_wf eu-segment_wf eu-seg-congruent_wf eu-congruent-transitivity eu-seg2_wf eu-seg1_wf sq_stable__eu-congruent
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation sqequalHypSubstitution cut lemma_by_obid dependent_functionElimination thin setElimination rename hypothesisEquality isectElimination hypothesis independent_functionElimination introduction because_Cache independent_isectElimination sqequalRule imageMemberEquality baseClosed imageElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[s1,s2,s3:Segment].    (s1  \mequiv{}  s3)  supposing  (s1  \mequiv{}  s2  and  s2  \mequiv{}  s3)

Date html generated: 2016_05_18-AM-06_36_46
Last ObjectModification: 2016_01_16-PM-10_30_43

Theory : euclidean!geometry

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