Nuprl Lemma : coSet-is-Set
∀[a:coSet{i:l}]. a ∈ Set{i:l} supposing isSet(a)
Proof
Definitions occuring in Statement :
isSet: isSet(w),
Set: Set{i:l},
coSet: coSet{i:l},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
coSet: coSet{i:l},
isSet: isSet(w),
Set: Set{i:l}
Lemmas referenced :
coW-is-W
Rules used in proof :
hypothesis,
hypothesisEquality,
lambdaEquality,
universeEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:coSet\{i:l\}]. a \mmember{} Set\{i:l\} supposing isSet(a)
Date html generated:
2018_07_29-AM-09_50_42
Last ObjectModification:
2018_07_24-PM-00_04_05
Theory : constructive!set!theory
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