Nuprl Lemma : stable__geo-between
∀g:EuclideanPlaneStructure. ∀[a,b,c:Point]. Stable{B(abc)}
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
geo-between: B(abc),
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
cand: A c∧ B,
and: P ∧ Q,
uimplies: b supposing a,
stable: Stable{P},
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-between: B(abc),
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
geo-gt-prim_wf,
geo-lsep_wf,
istype-void
Rules used in proof :
isectIsTypeImplies,
isect_memberEquality_alt,
functionIsTypeImplies,
dependent_functionElimination,
lambdaEquality_alt,
independent_pairEquality,
independent_pairFormation,
because_Cache,
applyEquality,
isectElimination,
universeIsType,
extract_by_obid,
hypothesisEquality,
inhabitedIsType,
functionIsType,
productIsType,
voidElimination,
hypothesis,
productElimination,
promote_hyp,
thin,
independent_functionElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation_alt,
sqequalRule,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlaneStructure. \mforall{}[a,b,c:Point]. Stable\{B(abc)\}
Date html generated:
2019_10_29-AM-09_13_10
Last ObjectModification:
2019_10_28-AM-09_51_19
Theory : euclidean!plane!geometry
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