### Nuprl Lemma : eu-congruence-identity2

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

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-congruent: `ab=cd` 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-congruent_wf eu-congruence-identity equal_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis equalitySymmetry 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,d:Point].    (a  =  b)  supposing  (ab=cd  and  (c  =  d))

Date html generated: 2016_10_26-AM-07_40_48
Last ObjectModification: 2016_07_12-AM-08_06_46

Theory : euclidean!geometry

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