Nuprl Lemma : sub-vs-point-subtype
∀[K:Rng]. ∀[vs:VectorSpace(K)]. ∀[P:Point(vs) ⟶ ℙ]. (Point((v:vs | P[v])) ⊆r Point(vs))
Proof
Definitions occuring in Statement :
sub-vs: (v:vs | P[v]),
vector-space: VectorSpace(K),
vs-point: Point(vs),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
function: x:A ⟶ B[x],
rng: Rng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vs-point: Point(vs),
sub-vs: (v:vs | P[v]),
mk-vs: mk-vs,
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ,
rng: Rng
Lemmas referenced :
rec_select_update_lemma,
istype-void,
subtype_rel_self,
vs-point_wf,
vector-space_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
lambdaEquality_alt,
setElimination,
rename,
hypothesisEquality,
setIsType,
because_Cache,
universeIsType,
applyEquality,
instantiate,
isectElimination,
universeEquality,
axiomEquality,
functionIsType,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[K:Rng]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[P:Point(vs) {}\mrightarrow{} \mBbbP{}]. (Point((v:vs | P[v])) \msubseteq{}r Point(vs))
Date html generated:
2019_10_31-AM-06_26_49
Last ObjectModification:
2019_08_12-PM-01_23_33
Theory : linear!algebra
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