Nuprl Lemma : basic-geo-not-left-and-right
∀g:EuclideanPlaneStructure. (BasicGeometryAxioms(g) ⇒ (∀a,b,c:Point. (a leftof bc ⇒ (¬a leftof cb))))
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
basic-geo-axioms: BasicGeometryAxioms(g),
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,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
geo-eq: a ≡ b,
basic-geo-axioms: BasicGeometryAxioms(g),
cand: A c∧ B,
geo-ge: ab ≥ cd,
guard: {T},
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
or: P ∨ Q
Latex:
\mforall{}g:EuclideanPlaneStructure
(BasicGeometryAxioms(g) {}\mRightarrow{} (\mforall{}a,b,c:Point. (a leftof bc {}\mRightarrow{} (\mneg{}a leftof cb))))
Date html generated:
2020_05_20-AM-09_42_50
Last ObjectModification:
2020_01_13-PM-02_50_27
Theory : euclidean!plane!geometry
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