Nuprl Lemma : geo-between-implies-colinear
∀e:EuclideanPlane. ∀[a,b,c:Point]. Colinear(a;b;c) supposing B(abc)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-colinear: Colinear(a;b;c),
geo-between: B(abc),
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-colinear: Colinear(a;b;c),
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
guard: {T},
geo-between: B(abc),
and: P ∧ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c:Point]. Colinear(a;b;c) supposing B(abc)
Date html generated:
2020_05_20-AM-09_47_40
Last ObjectModification:
2019_11_13-PM-03_28_05
Theory : euclidean!plane!geometry
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