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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