Nuprl Lemma : geo-congruent-transitivity
∀e:EuclideanPlane. ∀[a,b,c,d,x,y:Point]. (ab ≅ xy) supposing (cd ≅ xy and ab ≅ cd)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
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,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
and: P ∧ Q,
squash: ↓T,
geo-congruent: ab ≅ cd,
not: ¬A,
false: False,
guard: {T},
prop: ℙ
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d,x,y:Point]. (ab \mcong{} xy) supposing (cd \mcong{} xy and ab \mcong{} cd)
Date html generated:
2020_05_20-AM-09_45_28
Last ObjectModification:
2019_11_13-AM-10_45_42
Theory : euclidean!plane!geometry
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