Nuprl Lemma : symmetric-point-construction1
∀e:BasicGeometry. ∀a:Point. ∀p:{p:Point| a # p} . (∃p':Point [p=a=p'])
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
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 :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T,
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
geo-midpoint: a=m=b
Latex:
\mforall{}e:BasicGeometry. \mforall{}a:Point. \mforall{}p:\{p:Point| a \# p\} . (\mexists{}p':Point [p=a=p'])
Date html generated:
2020_05_20-AM-09_49_46
Last ObjectModification:
2020_01_27-PM-10_03_36
Theory : euclidean!plane!geometry
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