### Nuprl Lemma : eu-congruence-identity

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

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` euclidean-plane: `EuclideanPlane` prop: `ℙ` guard: `{T}` euclidean-axioms: `euclidean-axioms(e)` and: `P ∧ Q`
Lemmas referenced :  eu-congruent_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution setElimination thin rename hypothesis lemma_by_obid isectElimination hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry productElimination independent_isectElimination

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

Date html generated: 2016_05_18-AM-06_33_59
Last ObjectModification: 2015_12_28-AM-09_27_42

Theory : euclidean!geometry

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