Nuprl Lemma : geo-cong-angle_wf
∀[e:BasicGeometry]. ∀[a,b,c,x,y,z:Point].  (abc ≅a xyz ∈ ℙ)
Proof
Definitions occuring in Statement : 
geo-cong-angle: abc ≅a xyz
, 
basic-geometry: BasicGeometry
, 
geo-point: Point
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
geo-cong-angle: abc ≅a xyz
, 
prop: ℙ
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
exists: ∃x:A. B[x]
Lemmas referenced : 
geo-sep_wf, 
euclidean-plane-structure-subtype, 
euclidean-plane-subtype, 
basic-geometry-subtype, 
subtype_rel_transitivity, 
basic-geometry_wf, 
euclidean-plane_wf, 
euclidean-plane-structure_wf, 
geo-primitives_wf, 
exists_wf, 
geo-point_wf, 
geo-between_wf, 
geo-congruent_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
productEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
instantiate, 
independent_isectElimination, 
because_Cache, 
lambdaEquality_alt, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
inhabitedIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
universeIsType
Latex:
\mforall{}[e:BasicGeometry].  \mforall{}[a,b,c,x,y,z:Point].    (abc  \mcong{}\msuba{}  xyz  \mmember{}  \mBbbP{})
Date html generated:
2019_10_16-PM-01_22_02
Last ObjectModification:
2018_11_07-PM-00_52_23
Theory : euclidean!plane!geometry
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