Nuprl Lemma : geo-colinear-equidistant
∀e:BasicGeometry. ∀[a,b,c,p,q:Point]. (cp ≅ cq) supposing (ap ≅ aq and bp ≅ bq and Colinear(a;b;c) and a # b)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-congruent: ab ≅ cd,
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-congruent: ab ≅ cd,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry: BasicGeometry
Latex:
\mforall{}e:BasicGeometry
\mforall{}[a,b,c,p,q:Point]. (cp \mcong{} cq) supposing (ap \mcong{} aq and bp \mcong{} bq and Colinear(a;b;c) and a \# b)
Date html generated:
2020_05_20-AM-09_52_38
Last ObjectModification:
2019_12_20-PM-08_44_58
Theory : euclidean!plane!geometry
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