Nuprl Lemma : bind-class-program_wf
∀[Info,A,B:Type].
∀[X:EClass(A)]. ∀[Y:A ─→ EClass(B)]. ∀[xpr:LocalClass(X)]. ∀[ypr:a:A ─→ LocalClass(Y[a])].
(xpr >>= ypr ∈ LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
bind-class-program: xpr >>= ypr,
bind-class: X >x> Y[x],
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
local-class_wf,
equal_wf,
es-E_wf,
event-ordering+_subtype,
all_wf,
bag_wf,
class-ap_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
es-loc_wf,
map_wf,
es-info_wf,
es-before_wf,
hdataflow_wf,
set_wf,
Id_wf,
hdf-bind_wf,
bind-class_wf,
eclass_wf,
event-ordering+_wf,
valueall-type_wf,
es-le-before_wf2,
list_wf,
es-le_wf,
bag-combine_wf,
squash_wf,
true_wf,
list-subtype-bag,
subtype_rel_self,
eo-forward_wf,
member-eo-forward-E,
filter_wf5,
l_member_wf,
es-ble_wf,
iff_weakening_equal,
eo-forward-loc,
pi2_wf,
eo-forward-info,
map_functionality,
es-before_wf3,
subtype_rel_list,
es-locl_wf,
subtype_rel_set,
eo-forward-E-subtype,
eo-forward-before,
decidable__es-le,
es-le-loc,
and_wf,
es-le-before_wf,
iterate-hdf-bind-simple,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
map_nil_lemma,
filter_nil_lemma,
iter_hdf_nil_lemma,
bag_combine_empty_lemma,
simple-hdf-bind_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-pred_wf,
top_wf,
es-pred-locl,
es-causl_weakening,
cons_wf,
nil_wf,
map_cons_lemma,
iter_hdf_cons_lemma,
append_wf,
bag-map_wf,
simple-bind-nxt_wf,
map_append_sq,
iterate-hdf-append,
mk-hdf_wf,
valueall-type-has-valueall,
bag-valueall-type,
product-valueall-type,
hdataflow-valueall-type,
bag-append_wf,
evalall-reduce,
bag-map-map,
compose_wf,
bag-combine-append-left,
single-bag_wf,
bag-map-append,
bfalse_wf,
bag-filter-append,
filter_cons_lemma,
assert-es-ble,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-le_weakening,
bag-map-combine,
bag-combine-single-left,
filter_append_sq,
es-le_weakening_eq,
filter_is_nil,
l_all_iff,
es-locl_transitivity2,
es-locl_irreflexivity,
bag-combine-map,
bag-combine-combine
Latex:
\mforall{}[Info,A,B:Type].
\mforall{}[X:EClass(A)]. \mforall{}[Y:A {}\mrightarrow{} EClass(B)]. \mforall{}[xpr:LocalClass(X)]. \mforall{}[ypr:a:A {}\mrightarrow{} LocalClass(Y[a])].
(xpr >>= ypr \mmember{} LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Date html generated:
2015_07_22-PM-00_02_45
Last ObjectModification:
2015_02_04-PM-05_16_16
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