Nuprl Lemma : set-part_wf
∀[s:coSet{i:l}]. (set-part(s) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
set-part: set-part(s),
Set: Set{i:l},
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
pi1: fst(t),
prop: ℙ,
mk-set: f"(T),
Wsup: Wsup(a;b),
sub-set: {a ∈ s | P[a]},
set-part: set-part(s),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
coSet-is-Set,
isSet_wf,
mk-set_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_isectElimination,
lambdaEquality,
productEquality,
isectElimination,
thin,
productElimination,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:coSet\{i:l\}]. (set-part(s) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-09_52_38
Last ObjectModification:
2018_07_25-PM-03_50_26
Theory : constructive!set!theory
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