Nuprl Lemma : co-regext_wf
∀[a:coSet{i:l}]. (co-regext(a) ∈ coSet{i:l})
Proof
Definitions occuring in Statement : 
co-regext: co-regext(a)
, 
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]
, 
co-regext: co-regext(a)
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
coSet_wf, 
regextfun_wf, 
set-dom_wf, 
coW_wf, 
mk-coset_wf, 
coSet_subtype, 
subtype_coSet
Rules used in proof : 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
lambdaEquality, 
isectElimination, 
thin, 
productElimination, 
sqequalRule, 
sqequalHypSubstitution, 
applyEquality, 
hypothesisEquality, 
hypothesis, 
extract_by_obid, 
hypothesis_subsumption, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[a:coSet\{i:l\}].  (co-regext(a)  \mmember{}  coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_07_57
Last ObjectModification:
2018_07_21-PM-04_32_57
Theory : constructive!set!theory
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