Nuprl Lemma : eu-between-eq-same2

`∀[e:EuclideanPlane]. ∀[a,b,c:Point].  (a = b ∈ Point) supposing ((a = c ∈ Point) and a_b_c)`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-point: `Point` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  eu-between-eq_wf eu-between-eq-same equal_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut equalitySymmetry hypothesis thin hyp_replacement Error :applyLambdaEquality,  extract_by_obid sqequalHypSubstitution isectElimination setElimination rename because_Cache hypothesisEquality sqequalRule independent_isectElimination isect_memberEquality axiomEquality equalityTransitivity

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a,b,c:Point].    (a  =  b)  supposing  ((a  =  c)  and  a\_b\_c)

Date html generated: 2016_10_26-AM-07_40_55
Last ObjectModification: 2016_07_12-AM-08_06_54

Theory : euclidean!geometry

Home Index