Nuprl Lemma : Euclid-Prop31-sep
∀e:EuclideanPlane. ∀a,b,x:Point. (a # b ⇒ x # ab ⇒ (∃y:Point. (geo-parallel-points(e;a;b;x;y) ∧ x # y)))
Proof
Definitions occuring in Statement :
geo-parallel-points: geo-parallel-points(e;a;b;c;d),
euclidean-plane: EuclideanPlane,
geo-lsep: a # 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],
member: t ∈ T,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
geo-parallel-points: geo-parallel-points(e;a;b;c;d)
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,x:Point.
(a \# b {}\mRightarrow{} x \# ab {}\mRightarrow{} (\mexists{}y:Point. (geo-parallel-points(e;a;b;x;y) \mwedge{} x \# y)))
Date html generated:
2020_05_20-AM-10_43_46
Last ObjectModification:
2020_01_13-PM-10_28_28
Theory : euclidean!plane!geometry
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