Nuprl Lemma : eu-inner-five-segment'

∀e:EuclideanPlane
  ∀[a,b,c,A,B,C:Point].  (∀d,D:Point.  (bd=BD) supposing (cd=CD and ad=AD)) supposing (bc=BC and ac=AC and A_B_C and a_b\000C_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 :  euclidean-plane: EuclideanPlane,  prop: ℙ,  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  member: t ∈ T,  all: ∀x:A. B[x]
Lemmas referenced :  eu-inner-five-segment,  eu-congruent_wf,  eu-point_wf,  eu-between-eq_wf,  euclidean-plane_wf
Rules used in proof :  rename,  setElimination,  independent_isectElimination,  isectElimination,  isect_memberFormation,  hypothesisEquality,  thin,  dependent_functionElimination,  sqequalHypSubstitution,  hypothesis,  lambdaFormation,  sqequalReflexivity,  computationStep,  sqequalTransitivity,  sqequalSubstitution,  lemma_by_obid,  cut

Latex:
\mforall{}e:EuclideanPlane
    \mforall{}[a,b,c,A,B,C:Point].
        (\mforall{}d,D:Point.    (bd=BD)  supposing  (cd=CD  and  ad=AD))  supposing  (bc=BC  and  ac=AC  and  A\_B\_C  and  a\_b\_\000Cc)



Date html generated: 2016_05_18-AM-06_38_48
Last ObjectModification: 2016_01_02-PM-00_14_01

Theory : euclidean!geometry


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