Nuprl Lemma : Euclid-midpoint-1
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a # b} . (∃d:Point [a=d=b])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-midpoint: a=m=b,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
set: {x:A| B[x]}
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
sq_stable: SqStable(P),
euclidean-plane: EuclideanPlane,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
geo-gt-prim: ab>cd,
record-select: r.x,
geo-sep: a # b,
uiff: uiff(P;Q),
basic-geometry: BasicGeometry,
false: False,
basic-geometry-: BasicGeometry-,
iff: P ⇐⇒ Q,
true: True,
not: ¬A,
geo-eq: a ≡ b,
sq_exists: ∃x:A [B[x]],
geo-midpoint: a=m=b
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}b:\{b:Point| a \# b\} . (\mexists{}d:Point [a=d=b])
Date html generated:
2020_05_20-AM-10_03_07
Last ObjectModification:
2019_12_26-PM-08_57_05
Theory : euclidean!plane!geometry
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