Nuprl Lemma : Euclid-Prop23_half-plane2
∀e:EuclideanPlane. ∀a,b,x,y,z:Point. (z # xy ⇒ a # b ⇒ (∃x',b':Point. (out(a bb') ∧ x' leftof b'a ∧ x'ab' ≅a zxy)))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
geo-cong-angle: abc ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-left: a leftof bc,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
geo-out: out(p ab),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
basic-geometry: BasicGeometry,
squash: ↓T,
sq_stable: SqStable(P),
geo-cong-angle: abc ≅a xyz,
uiff: uiff(P;Q)
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,x,y,z:Point.
(z \# xy {}\mRightarrow{} a \# b {}\mRightarrow{} (\mexists{}x',b':Point. (out(a bb') \mwedge{} x' leftof b'a \mwedge{} x'ab' \mcong{}\msuba{} zxy)))
Date html generated:
2020_05_20-AM-10_40_59
Last ObjectModification:
2020_01_13-PM-05_16_58
Theory : euclidean!plane!geometry
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