Nuprl Lemma : sys-antecedent-closure
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀fs:sys-antecedent(es;X) List. ∀s:fset(E(X)). ∃c:fset(E(X)). (c = fs closure of s)
Proof
Definitions occuring in Statement :
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
fset-closure: (c = fs closure of s),
fset: fset(T),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
universe: Type
Lemmas :
l_all_iff,
sys-antecedent_wf,
l_member_wf,
all_wf,
es-E-interface_wf,
not_wf,
equal_wf,
less_than_wf,
nat_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
list_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
nil_wf,
cons_wf,
set_wf,
es-causle_wf,
and_wf,
in-eclass_wf,
assert_elim,
bool_wf,
bool_subtype_base,
assert_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}fs:sys-antecedent(es;X) List. \mforall{}s:fset(E(X)).
\mexists{}c:fset(E(X)). (c = fs closure of s)
Date html generated:
2015_07_17-PM-00_55_25
Last ObjectModification:
2015_01_27-PM-10_50_44
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