Nuprl Lemma : set-item_wf
∀[s:coSet{i:l}]. ∀[x:set-dom(s)]. (set-item(s;x) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
set-item: set-item(s;x),
set-dom: set-dom(s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
set-item: set-item(s;x),
set-dom: set-dom(s),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
set-dom_wf,
coSet_wf,
pi2_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
functionEquality,
lambdaEquality,
universeEquality,
isectElimination,
instantiate,
thin,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:coSet\{i:l\}]. \mforall{}[x:set-dom(s)]. (set-item(s;x) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-09_49_38
Last ObjectModification:
2018_07_11-AM-11_16_24
Theory : constructive!set!theory
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