Nuprl Lemma : isSet_wf
∀[a:coSet{i:l}]. (isSet(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
isSet: isSet(w),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
coSet: coSet{i:l},
so_apply: x[s],
so_lambda: λ2x.t[x],
isSet: isSet(w),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
coW-wfdd_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
universeEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:coSet\{i:l\}]. (isSet(a) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-09_50_37
Last ObjectModification:
2018_07_24-PM-00_03_53
Theory : constructive!set!theory
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