Nuprl Lemma : eu-cong-angle_wf

`∀[e:EuclideanPlane]. ∀[a,b,c,x,y,z:Point].  (abc = xyz ∈ ℙ)`

Proof

Definitions occuring in Statement :  eu-cong-angle: `abc = xyz` 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-angle: `abc = xyz` prop: `ℙ` and: `P ∧ Q` euclidean-plane: `EuclideanPlane` so_lambda: `λ2x.t[x]` so_apply: `x[s]` exists: `∃x:A. B[x]`
Lemmas referenced :  not_wf equal_wf eu-point_wf exists_wf eu-between-eq_wf eu-congruent_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[a,b,c,x,y,z:Point].    (abc  =  xyz  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-06_41_50
Last ObjectModification: 2015_12_28-AM-09_23_09

Theory : euclidean!geometry

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