Nuprl Lemma : stable__geo-out-strict
∀[e:BasicGeometry]. ∀[a,b:Point]. ∀p:Point. Stable{geo-out-strict(e;p;a;b)}
Proof
Definitions occuring in Statement :
geo-out-strict: geo-out-strict(e;p;a;b),
basic-geometry: BasicGeometry,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
false: False,
implies: P ⇒ Q,
not: ¬A,
stable: Stable{P},
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
geo-out-strict: geo-out-strict(e;p;a;b),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-out-strict_wf,
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-strict-between_wf,
not_wf,
stable__not
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
dependent_functionElimination,
lambdaEquality,
because_Cache,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. \mforall{}p:Point. Stable\{geo-out-strict(e;p;a;b)\}
Date html generated:
2017_10_02-PM-06_25_25
Last ObjectModification:
2017_08_05-PM-04_19_00
Theory : euclidean!plane!geometry
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