Nuprl Lemma : geo-colinear-implies-between-or
∀e:EuclideanPlane. ∀a,b,c:Point. (Colinear(a;b;c) ⇒ (¬¬((B(acb) ∨ B(bac)) ∨ B(abc))))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-colinear: Colinear(a;b;c),
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
oriented-plane: OrientedPlane,
uimplies: b supposing a,
guard: {T}
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (Colinear(a;b;c) {}\mRightarrow{} (\mneg{}\mneg{}((B(acb) \mvee{} B(bac)) \mvee{} B(abc))))
Date html generated:
2020_05_20-AM-09_50_40
Last ObjectModification:
2019_12_23-AM-10_11_53
Theory : euclidean!plane!geometry
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