Nuprl Lemma : subtype-set-hasloc
∀[i:Id]. ∀[d:{k:Knd| ↑hasloc(k;i)} List]. ({k:Knd| (k ∈ d)} ⊆r {k:{k:Knd| ↑hasloc(k;i)} | (k ∈ d)} )
Proof
Definitions occuring in Statement :
hasloc: hasloc(k;i),
Knd: Knd,
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Lemmas :
list_wf,
Knd_wf,
assert_wf,
hasloc_wf,
Id_wf,
l_member_wf,
subtype_rel_list,
l_member-settype,
l_member-set2,
subtype_rel_nested_set,
subtype_rel_sets,
subtype_base_sq,
union_subtype_base,
IdLnk_wf,
product_subtype_base,
atom2_subtype_base,
select_wf,
sq_stable__le,
set_wf,
assert_elim,
bool_wf,
bool_subtype_base,
equal_wf
\mforall{}[i:Id]. \mforall{}[d:\{k:Knd| \muparrow{}hasloc(k;i)\} List]. (\{k:Knd| (k \mmember{} d)\} \msubseteq{}r \{k:\{k:Knd| \muparrow{}hasloc(k;i)\} | (k \mmember{} d)\000C\} )
Date html generated:
2015_07_17-AM-09_14_04
Last ObjectModification:
2015_01_28-AM-07_55_32
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