### Nuprl Lemma : eu-congruence-identity-sym

`∀[e:EuclideanPlane]. ∀[a,b,c:Point].  a = b ∈ Point supposing cc=ab`

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` all: `∀x:A. B[x]`
Lemmas referenced :  eu-congruent_wf eu-point_wf euclidean-plane_wf eu-congruent-symmetry eu-congruence-identity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination independent_isectElimination

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a,b,c:Point].    a  =  b  supposing  cc=ab

Date html generated: 2016_05_18-AM-06_35_09
Last ObjectModification: 2015_12_28-AM-09_26_14

Theory : euclidean!geometry

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