### Nuprl Lemma : eu-cong-tri_wf

`∀[e:EuclideanPlane]. ∀[a,b,c,a',b',c':Point].  (Cong3(abc,a'b'c') ∈ ℙ)`

Proof

Definitions occuring in Statement :  eu-cong-tri: `Cong3(abc,a'b'c')` euclidean-plane: `EuclideanPlane` eu-point: `Point` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` eu-cong-tri: `Cong3(abc,a'b'c')` euclidean-plane: `EuclideanPlane`
Lemmas referenced :  and_wf eu-congruent_wf eu-point_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a,b,c,a',b',c':Point].    (Cong3(abc,a'b'c')  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-06_41_55
Last ObjectModification: 2015_12_28-AM-09_22_50

Theory : euclidean!geometry

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