Nuprl Lemma : set-item_wf2
∀[s:Set{i:l}]. ∀[t:set-dom(s)]. (set-item(s;t) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
Set: Set{i:l},
set-item: set-item(s;x),
set-dom: set-dom(s),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
top: Top,
all: ∀x:A. B[x],
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,
set-subtype-coSet,
set-dom_wf,
item_mk_set_lemma,
dom_mk_set_lemma,
set-subtype,
subtype-set
Rules used in proof :
isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
rename,
thin,
productElimination,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
introduction,
hypothesis_subsumption,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:Set\{i:l\}]. \mforall{}[t:set-dom(s)]. (set-item(s;t) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-09_50_49
Last ObjectModification:
2018_07_11-PM-09_56_41
Theory : constructive!set!theory
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