### Nuprl Lemma : eu-seg-length-test2

`∀e:EuclideanPlane. ∀s1,s2:ProperSegment. ∀t1,t2,t3:Segment.  (s1 ≡ s2 `` t1 ≡ t2 `` t2 ≡ t3 `` s1 + t1 ≡ s2 + t3)`

Proof

Definitions occuring in Statement :  eu-seg-extend: `s + t` eu-seg-congruent: `s1 ≡ s2` eu-proper-segment: `ProperSegment` eu-segment: `Segment` euclidean-plane: `EuclideanPlane` all: `∀x:A. B[x]` implies: `P `` Q`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` prop: `ℙ` euclidean-plane: `EuclideanPlane` eu-proper-segment: `ProperSegment`
Lemmas referenced :  eu-seg-extend_functionality eu-seg-congruent-iff-length eu-seg-congruent_wf eu-segment_wf eu-proper-segment_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality isectElimination independent_isectElimination hypothesis because_Cache productElimination equalityTransitivity setElimination rename

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}s1,s2:ProperSegment.  \mforall{}t1,t2,t3:Segment.
(s1  \mequiv{}  s2  {}\mRightarrow{}  t1  \mequiv{}  t2  {}\mRightarrow{}  t2  \mequiv{}  t3  {}\mRightarrow{}  s1  +  t1  \mequiv{}  s2  +  t3)

Date html generated: 2016_05_18-AM-06_41_21
Last ObjectModification: 2015_12_28-AM-09_23_18

Theory : euclidean!geometry

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