Nuprl Lemma : Dsep-iff-sep
∀e:EuclideanPlane. ∀a,b:Point. (Dsep(e;a;b) ⇐⇒ a # b)
Proof
Definitions occuring in Statement :
dist-sep: Dsep(g;a;b),
euclidean-plane: EuclideanPlane,
geo-sep: a # b,
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],
prop: ℙ,
rev_implies: P ⇐ Q,
dist-sep: Dsep(g;a;b),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
squash: ↓T,
true: True
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. (Dsep(e;a;b) \mLeftarrow{}{}\mRightarrow{} a \# b)
Date html generated:
2020_05_20-AM-10_49_09
Last ObjectModification:
2020_01_13-PM-06_32_35
Theory : euclidean!plane!geometry
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