Nuprl Lemma : geo-between-outer-trans2-cpy
∀e:EuclideanPlane. ∀[a,b,c,d:Point]. (B(abd)) supposing (B(bcd) and B(abc) and b # c)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-between: B(abc),
geo-sep: a # b,
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,
and: P ∧ Q,
implies: P ⇒ Q,
geo-between: B(abc),
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b,c,d:Point]. (B(abd)) supposing (B(bcd) and B(abc) and b \# c)
Date html generated:
2020_05_20-AM-09_50_52
Last ObjectModification:
2019_12_20-PM-08_45_49
Theory : euclidean!plane!geometry
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