Nuprl Lemma : geo-gt-prim-ge-trans
∀e:EuclideanPlane. ∀a,b,c,d,f,g:Point. (ab>cd ⇒ cd ≥ fg ⇒ ab>fg)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-ge: ab ≥ cd,
geo-gt-prim: ab>cd,
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,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d,f,g:Point. (ab>cd {}\mRightarrow{} cd \mgeq{} fg {}\mRightarrow{} ab>fg)
Date html generated:
2020_05_20-AM-09_45_01
Last ObjectModification:
2019_12_23-AM-08_51_06
Theory : euclidean!plane!geometry
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