Nuprl Lemma : not-out-if-lsep
∀g:EuclideanPlane. ∀a,b,c:Point. (a # bc ⇒ (¬out(b ac)))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
euclidean-plane: EuclideanPlane,
geo-lsep: a # 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],
basic-geometry: BasicGeometry,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
not-lsep-if-out,
geo-out_wf,
geo-lsep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
voidElimination,
because_Cache,
universeIsType,
isectElimination,
sqequalRule,
applyEquality,
instantiate,
independent_isectElimination,
inhabitedIsType
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (a \# bc {}\mRightarrow{} (\mneg{}out(b ac)))
Date html generated:
2019_10_16-PM-01_23_25
Last ObjectModification:
2019_09_27-PM-05_55_10
Theory : euclidean!plane!geometry
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