Nuprl Lemma : left-not-colinear
∀g:EuclideanPlane. ∀a,b,c:Point.  (a leftof cb ⇒ (¬Colinear(a;b;c)))
Proof
Definitions occuring in Statement : 
euclidean-plane: EuclideanPlane, 
geo-colinear: Colinear(a;b;c), 
geo-left: a leftof bc, 
geo-point: Point, 
all: ∀x:A. B[x], 
not: ¬A, 
implies: P ⇒ Q
Definitions unfolded in proof : 
all: ∀x:A. B[x], 
implies: P ⇒ Q, 
not: ¬A, 
false: False, 
geo-colinear: Colinear(a;b;c), 
member: t ∈ T, 
guard: {T}, 
and: P ∧ Q, 
cand: A c∧ B, 
uall: ∀[x:A]. B[x], 
subtype_rel: A ⊆r B, 
uimplies: b supposing a, 
prop: ℙ
Latex:
\mforall{}g:EuclideanPlane.  \mforall{}a,b,c:Point.    (a  leftof  cb  {}\mRightarrow{}  (\mneg{}Colinear(a;b;c)))
Date html generated:
2020_05_20-AM-09_48_09
Last ObjectModification:
2019_11_13-PM-01_56_19
Theory : euclidean!plane!geometry
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