Nuprl Lemma : not-left-collinear
∀g:OrientedPlane. ∀a,b,c:Point. ((¬a leftof bc) ⇒ (¬a leftof cb) ⇒ (¬((¬B(abc)) ∧ (¬B(bca)) ∧ (¬B(cab)))))
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-between: B(abc),
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oriented-plane: OrientedPlane,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
uimplies: b supposing a,
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
or: P ∨ Q,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,c:Point.
((\mneg{}a leftof bc) {}\mRightarrow{} (\mneg{}a leftof cb) {}\mRightarrow{} (\mneg{}((\mneg{}B(abc)) \mwedge{} (\mneg{}B(bca)) \mwedge{} (\mneg{}B(cab)))))
Date html generated:
2020_05_20-AM-09_50_05
Last ObjectModification:
2019_12_20-PM-07_37_36
Theory : euclidean!plane!geometry
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