Nuprl Lemma : set-dom_wf
∀[s:coSet{i:l}]. (set-dom(s) ∈ Type)
Proof
Definitions occuring in Statement :
set-dom: set-dom(s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
set-dom: set-dom(s),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
pi1_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
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\}]. (set-dom(s) \mmember{} Type)
Date html generated:
2018_07_29-AM-09_49_36
Last ObjectModification:
2018_07_11-AM-11_15_05
Theory : constructive!set!theory
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