Nuprl Lemma : geo-left-antisymmetry
∀g:OrientedPlane. ∀a,b,c:Point. (a leftof bc ⇒ (¬a leftof cb))
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
oriented-plane: Error :oriented-plane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
Error :oriented-plane_wf,
subtype_rel_transitivity,
Error :oriented-plane-subtype,
basic-geometry--subtype,
geo-point_wf,
geo-left_wf,
not-left-and-right
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
rename,
setElimination,
isectElimination,
voidElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,c:Point. (a leftof bc {}\mRightarrow{} (\mneg{}a leftof cb))
Date html generated:
2017_10_02-PM-06_49_22
Last ObjectModification:
2017_08_06-PM-07_29_14
Theory : euclidean!plane!geometry
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