Nuprl Lemma : set-ss_wf
∀[ss:SeparationSpace]. ∀[P:Point(ss) ⟶ ℙ]. ({x:ss | P[x]} ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
set-ss: {x:ss | P[x]},
ss-point: Point(ss),
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
separation-space: SeparationSpace,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
set-ss: {x:ss | P[x]},
not: ¬A,
false: False,
guard: {T},
uimplies: b supposing a,
ss-point: Point(ss),
ss-sep: x # y
Lemmas referenced :
subtype_rel_self,
record-select_wf,
top_wf,
istype-atom,
not_wf,
all_wf,
or_wf,
mk-ss_wf,
ss-point_wf,
ss-sep_wf,
ss-sep-irrefl,
istype-void,
subtype_rel_dep_function,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
setEquality,
functionEquality,
cumulativity,
lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
because_Cache,
applyLambdaEquality,
setElimination,
rename,
inhabitedIsType,
universeIsType,
dependent_set_memberEquality_alt,
setIsType,
lambdaFormation_alt,
independent_functionElimination,
voidElimination,
functionIsType,
unionEquality,
independent_isectElimination,
unionIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[P:Point(ss) {}\mrightarrow{} \mBbbP{}]. (\{x:ss | P[x]\} \mmember{} SeparationSpace)
Date html generated:
2019_10_31-AM-07_26_52
Last ObjectModification:
2019_09_19-PM-04_10_14
Theory : constructive!algebra
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