Nuprl Lemma : loop-class-state-program_wf
∀[Info,B:Type].
∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[pr:LocalClass(X)].
(loop-class-state-program(pr;init) ∈ LocalClass(loop-class-state(X;init)))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
loop-class-state-program: loop-class-state-program(pr;init),
loop-class-state: loop-class-state(X;init),
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],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-E_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,
primed-class-opt-cases,
loop-class-state_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
subtype_top,
Id_wf,
bag_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
map_nil_lemma,
iter_hdf_nil_lemma,
hdf-state_wf,
es-loc_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
map_wf,
es-info_wf,
es-before_wf,
es-pred_wf,
subtype_rel_list,
map_cons_lemma,
iter_hdf_cons_lemma,
es-pred-locl,
es-causl_weakening,
class-ap_wf,
primed-class-opt_wf,
hdf-ap_wf,
iterate-hdataflow_wf,
lt_int_wf,
bag-size_wf,
assert_of_lt_int,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
map_append_sq,
iterate-hdf-append,
squash_wf,
true_wf,
list_wf,
hdataflow_wf,
valueall-type_wf,
es-loc-pred,
iff_weakening_equal,
atom2_subtype_base,
es-pred-loc-base,
hdataflow-ext,
unit_wf2,
bag_combine_empty_lemma,
bag_null_empty_lemma,
valueall-type-has-valueall,
bag-valueall-type,
bag-combine_wf,
bag-map_wf,
evalall-reduce,
bag-null_wf,
assert-bag-null,
hdf-run_wf,
le_int_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
iff_transitivity,
iff_weakening_uiff,
eq_int_wf,
neg_assert_of_eq_int,
bag_size_empty_lemma,
assert_of_eq_int,
ifthenelse_wf,
bool_cases,
bag-size-zero,
empty-bag_wf,
member-eclass_wf,
and_wf,
pi2_wf,
assert_elim,
not_assert_elim,
btrue_neq_bfalse,
not-not-assert,
null-bag-size,
hdf_ap_halt_lemma,
lifting-strict-spread,
strict4-spread,
lifting-strict-callbyvalueall,
bag-combine-null,
bag-size-bag-member,
bag-map-null,
bag_map_empty_lemma,
bag-combine-empty-right
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[pr:LocalClass(X)].
(loop-class-state-program(pr;init) \mmember{} LocalClass(loop-class-state(X;init)))
supposing valueall-type(B)
Date html generated:
2015_07_22-PM-00_03_09
Last ObjectModification:
2015_02_04-PM-05_14_20
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