Nuprl Lemma : extended-out-preserves-between
∀e:EuclideanPlane. ∀a,b,c,d:Point. ((out(a bc) ∧ b-a-d) ⇒ c-a-d)
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
euclidean-plane: EuclideanPlane,
geo-strict-between: a-b-c,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
geo-out: out(p ab),
exists: ∃x:A. B[x],
basic-geometry-: BasicGeometry-,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. ((out(a bc) \mwedge{} b-a-d) {}\mRightarrow{} c-a-d)
Date html generated:
2020_05_20-AM-09_55_47
Last ObjectModification:
2020_01_13-PM-03_29_18
Theory : euclidean!plane!geometry
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