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
Home
Index