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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