Nuprl Lemma : regext_wf
∀[a:coSet{i:l}]. (regext(a) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
regext: 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],
mk-coset: mk-coset(T;f),
Wsup: Wsup(a;b),
mk-set: f"(T),
regext: regext(a),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
set-dom_wf,
W_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\}]. (regext(a) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_07_15
Last ObjectModification:
2018_07_20-AM-10_52_44
Theory : constructive!set!theory
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