Nuprl Lemma : geo-congruent-sep
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab ≅ cd ⇒ c # d ⇒ a # b)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
geo-ge: ab ≥ cd,
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd),
not: ¬A,
or: P ∨ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab \mcong{} cd {}\mRightarrow{} c \# d {}\mRightarrow{} a \# b)
Date html generated:
2020_05_20-AM-09_46_29
Last ObjectModification:
2019_11_13-AM-10_45_46
Theory : euclidean!plane!geometry
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