Nuprl Lemma : geo-gt-prim-iff-lt
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab>cd ⇐⇒ |cd| < |ab|)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab>cd \mLeftarrow{}{}\mRightarrow{} |cd| < |ab|)
Date html generated:
2020_05_20-AM-10_01_02
Last ObjectModification:
2020_01_24-PM-01_56_27
Theory : euclidean!plane!geometry
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