Nuprl Lemma : isSet-set-predicate
∀s:coSet{i:l}. set-predicate{i:l}(s;x.isSet(x))
Proof
Definitions occuring in Statement :
set-predicate: set-predicate{i:l}(s;a.P[a]),
isSet: isSet(w),
coSet: coSet{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
iff: P ⇐⇒ Q,
member: t ∈ T,
implies: P ⇒ Q,
set-predicate: set-predicate{i:l}(s;a.P[a]),
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
seteq_wf,
isSet_wf,
isSet_functionality
Rules used in proof :
isectElimination,
productElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}s:coSet\{i:l\}. set-predicate\{i:l\}(s;x.isSet(x))
Date html generated:
2018_07_29-AM-09_52_15
Last ObjectModification:
2018_07_25-PM-03_40_56
Theory : constructive!set!theory
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