Nuprl Lemma : lsep-not-between
∀g:OrientedPlane. ∀a,b,c:Point.  (a # bc 
⇒ (¬a_b_c))
Proof
Definitions occuring in Statement : 
oriented-plane: OrientedPlane
, 
geo-lsep: a # bc
, 
geo-between: a_b_c
, 
geo-point: Point
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
oriented-plane: Error :oriented-plane, 
guard: {T}
, 
prop: ℙ
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
or: P ∨ Q
, 
geo-lsep: a # bc
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
geo-point_wf, 
geo-lsep_wf, 
Error :basic-geo-primitives_wf, 
Error :basic-geo-structure_wf, 
Error :o-geo-structure_wf, 
Error :oriented-plane_wf, 
subtype_rel_transitivity, 
Error :oriented-plane-subtype1, 
Error :o-geo-structure-subtype, 
geo-between_wf, 
Error :oriented-plane-subtype, 
geo-between-symmetry, 
left-not-between, 
left-symmetry
Rules used in proof : 
rename, 
setElimination, 
instantiate, 
voidElimination, 
independent_isectElimination, 
isectElimination, 
sqequalRule, 
applyEquality, 
because_Cache, 
hypothesis, 
independent_functionElimination, 
hypothesisEquality, 
dependent_functionElimination, 
extract_by_obid, 
introduction, 
unionElimination, 
sqequalHypSubstitution, 
thin, 
cut, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}g:OrientedPlane.  \mforall{}a,b,c:Point.    (a  \#  bc  {}\mRightarrow{}  (\mneg{}a\_b\_c))
Date html generated:
2017_10_02-PM-04_46_49
Last ObjectModification:
2017_08_05-AM-10_19_36
Theory : euclidean!plane!geometry
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