### Nuprl Lemma : eu-inner-three-segment

`∀e:EuclideanPlane. ∀[a,b,c,A,B,C:Point].  (ab=AB) supposing (bc=BC and ac=AC and A_B_C and a_b_c)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `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 :  member: `t ∈ T` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` prop: `ℙ` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  eu-congruent-trivial eu-congruent-iff-length eu-length-flip eu-inner-five-segment eu-congruent_wf eu-between-eq_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity hypothesisEquality hypothesis cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin isectElimination because_Cache productElimination independent_isectElimination equalityTransitivity equalitySymmetry lambdaFormation isect_memberFormation setElimination rename

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}[a,b,c,A,B,C:Point].    (ab=AB)  supposing  (bc=BC  and  ac=AC  and  A\_B\_C  and  a\_b\_c)

Date html generated: 2016_05_18-AM-06_38_51
Last ObjectModification: 2015_12_28-AM-09_24_01

Theory : euclidean!geometry

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