Nuprl Lemma : ss-basic-whole_wf
∀[X:SeparationSpace]. (ss-basic-whole() ∈ ss-basic(X))
Proof
Definitions occuring in Statement :
ss-basic-whole: ss-basic-whole(),
ss-basic: ss-basic(X),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
real-ss: ℝ,
ss-point: Point(ss),
mk-ss: Point=P #=Sep cotrans=C,
all: ∀x:A. B[x],
member: t ∈ T,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
ss-basic-whole: ss-basic-whole(),
ss-basic: ss-basic(X)
Lemmas referenced :
rec_select_update_lemma,
int-to-real_wf,
cons_wf,
ss-point_wf,
ss-fun_wf,
real-ss_wf,
real_wf,
ss-const_wf,
nil_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
isectElimination,
natural_numberEquality,
productEquality,
hypothesisEquality,
independent_pairEquality,
universeIsType
Latex:
\mforall{}[X:SeparationSpace]. (ss-basic-whole() \mmember{} ss-basic(X))
Date html generated:
2020_05_20-PM-01_22_13
Last ObjectModification:
2020_02_08-AM-11_38_59
Theory : intuitionistic!topology
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