Nuprl Lemma : regext_wf2
∀[a:Set{i:l}]. (regext(a) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
regext: regext(a),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
regext: regext(a),
Wsup: Wsup(a;b),
mk-set: f"(T),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Set_wf,
regextfun_wf2,
set-subtype-coSet,
set-dom_wf,
W_wf,
mk-set_wf,
set-subtype,
subtype-set
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
lambdaEquality,
isectElimination,
rename,
thin,
productElimination,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:Set\{i:l\}]. (regext(a) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_07_18
Last ObjectModification:
2018_07_20-AM-10_52_56
Theory : constructive!set!theory
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