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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