Nuprl Lemma : eclass0-bag-program_wf
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[F:Id ─→ bag(B) ─→ bag(C)]. ∀[Xpr:LocalClass(X)].
(eclass0-bag-program(F;Xpr) ∈ LocalClass(eclass0-bag(F;X))) supposing
((∀i:Id. ((F i {}) = {} ∈ bag(C))) and
valueall-type(C))
Proof
Definitions occuring in Statement :
eclass0-bag-program: eclass0-bag-program(f;pr),
eclass0-bag: eclass0-bag(f;X),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
empty-bag: {},
bag: bag(T)
Lemmas :
hdf-compose0-bag_wf,
es-E_wf,
event-ordering+_subtype,
all_wf,
equal_wf,
bag_wf,
class-ap_wf,
eclass0-bag_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
map_wf,
es-info_wf,
es-before_wf,
hdataflow_wf,
Id_wf,
equal-wf-T-base,
empty-bag_wf,
valueall-type_wf,
local-class_wf,
eclass_wf,
event-ordering+_wf,
iff_weakening_equal,
list_wf,
list_induction,
hdataflow-ext,
unit_wf2,
iter_hdf_nil_lemma,
valueall-type-has-valueall,
bag-valueall-type,
evalall-reduce,
iter_hdf_cons_lemma,
subtype_rel_list,
top_wf,
iterate-hdf-halt
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[F:Id {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C)]. \mforall{}[Xpr:LocalClass(X)].
(eclass0-bag-program(F;Xpr) \mmember{} LocalClass(eclass0-bag(F;X))) supposing
((\mforall{}i:Id. ((F i \{\}) = \{\})) and
valueall-type(C))
Date html generated:
2015_07_22-PM-00_01_56
Last ObjectModification:
2015_02_04-PM-05_11_00
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