Nuprl Lemma : geo-parallel-points-symmetry
∀e:EuclideanPlane. ∀a,b,c,d:Point. (geo-parallel-points(e;a;b;c;d) ⇒ geo-parallel-points(e;c;d;a;b))
Proof
Definitions occuring in Statement :
geo-parallel-points: geo-parallel-points(e;a;b;c;d),
euclidean-plane: EuclideanPlane,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
member: t ∈ T,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point.
(geo-parallel-points(e;a;b;c;d) {}\mRightarrow{} geo-parallel-points(e;c;d;a;b))
Date html generated:
2020_05_20-AM-10_05_09
Last ObjectModification:
2020_01_13-PM-10_23_08
Theory : euclidean!plane!geometry
Home
Index