Nuprl Lemma : geo-lt-or2
∀e:EuclideanPlane. ∀a,b,c,d:Point. (|ab| < |ac| ⇒ (|ab| < |ad| ∨ |ad| < |ac|))
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (|ab| < |ac| {}\mRightarrow{} (|ab| < |ad| \mvee{} |ad| < |ac|))
Date html generated:
2020_05_20-AM-10_50_46
Last ObjectModification:
2020_01_13-PM-06_14_00
Theory : euclidean!plane!geometry
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