Nuprl Lemma : geo-between-out
∀e:BasicGeometry. ∀a,b,c:Point.  (a # b ⇒ a # c ⇒ B(abc) ⇒ out(a bc))
Proof
Definitions occuring in Statement : 
geo-out: out(p ab), 
basic-geometry: BasicGeometry, 
geo-between: B(abc), 
geo-sep: a # b, 
geo-point: Point, 
all: ∀x:A. B[x], 
implies: P ⇒ Q
Definitions unfolded in proof : 
all: ∀x:A. B[x], 
implies: P ⇒ Q, 
geo-between: B(abc), 
geo-out: out(p ab), 
and: P ∧ Q, 
cand: A c∧ B, 
not: ¬A, 
member: t ∈ T, 
uall: ∀[x:A]. B[x], 
subtype_rel: A ⊆r B, 
prop: ℙ, 
false: False, 
guard: {T}, 
uimplies: b supposing a
Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c:Point.    (a  \#  b  {}\mRightarrow{}  a  \#  c  {}\mRightarrow{}  B(abc)  {}\mRightarrow{}  out(a  bc))
Date html generated:
2020_05_20-AM-09_55_05
Last ObjectModification:
2019_12_23-AM-10_14_08
Theory : euclidean!plane!geometry
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