Nuprl Lemma : set-ss_wf
∀[ss:SeparationSpace]. ∀[P:Point ⟶ ℙ]. (set-ss(ss;x.P[x]) ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
set-ss: set-ss(ss;x.P[x]),
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
ss-sep: x # y,
ss-point: Point,
uimplies: b supposing a,
false: False,
not: ¬A,
set-ss: set-ss(ss;x.P[x]),
or: P ∨ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
separation-space: SeparationSpace,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
subtype_rel_dep_function,
set_wf,
ss-sep-irrefl,
ss-sep_wf,
ss-point_wf,
mk-ss_wf,
or_wf,
not_wf,
all_wf,
subtype_rel_self
Rules used in proof :
isect_memberEquality,
axiomEquality,
dependent_functionElimination,
independent_isectElimination,
voidElimination,
independent_functionElimination,
lambdaFormation,
dependent_set_memberEquality,
rename,
setElimination,
functionExtensionality,
because_Cache,
cumulativity,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
functionEquality,
setEquality,
universeEquality,
isectElimination,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
hypothesisEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[P:Point {}\mrightarrow{} \mBbbP{}]. (set-ss(ss;x.P[x]) \mmember{} SeparationSpace)
Date html generated:
2016_11_08-AM-09_12_05
Last ObjectModification:
2016_11_02-AM-11_58_22
Theory : inner!product!spaces
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