Nuprl Lemma : eu-five-segment'

    (∀d,D:Point.  (cd=CD) supposing (bd=BD and ad=AD)) supposing 
       (bc=BC and 
       ab=AB and 
       A_B_C and 
       a_b_c and 
       (a b ∈ Point)))


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-congruent: ab=cd eu-point: Point uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] not: ¬A equal: t ∈ T
Definitions unfolded in proof :  prop: euclidean-plane: EuclideanPlane false: False implies:  Q not: ¬A member: t ∈ T uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x]
Lemmas referenced :  eu-point_wf eu-five-segment eu-congruent_wf eu-between-eq_wf not_wf equal_wf euclidean-plane_wf
Rules used in proof :  independent_isectElimination hypothesis rename setElimination isectElimination lemma_by_obid equalityEquality voidElimination hypothesisEquality thin dependent_functionElimination lambdaEquality sqequalHypSubstitution sqequalRule introduction cut isect_memberFormation lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

        (\mforall{}d,D:Point.    (cd=CD)  supposing  (bd=BD  and  ad=AD))  supposing 
              (bc=BC  and 
              ab=AB  and 
              A\_B\_C  and 
              a\_b\_c  and 
              (\mneg{}(a  =  b)))

Date html generated: 2016_05_18-AM-06_35_17
Last ObjectModification: 2016_01_02-PM-00_16_04

Theory : euclidean!geometry

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