Nuprl Lemma : local-class-equality
∀[Info,A:Type]. ∀[X:EClass(A)].
∀p,q:LocalClass(X).
p = q ∈ (Id ─→ hdataflow(Info;A))
supposing ∀i:Id. ∀inputs:Info List. hdf-halted(p i*(inputs)) = hdf-halted(q i*(inputs))
Proof
Definitions occuring in Statement :
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
list: T List,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B)
Lemmas :
hdataflow-equal,
bool_wf,
hdf-halted_wf,
iterate-hdataflow_wf,
iff_weakening_equal,
list_wf,
Id_wf,
all_wf,
equal_wf,
local-class_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
subtype_base_sq,
atom2_subtype_base,
bag_wf,
hdf-out_wf,
list2extended-eo,
assert_of_lt_int,
length_wf,
length_nil,
non_neg_length,
nil_wf,
length_wf_nil,
length_wf_nat,
length_cons,
length_append,
subtype_rel_list,
top_wf,
assert_wf,
lt_int_wf,
es-loc_wf,
map_wf,
es-info_wf,
es-before_wf,
length-map,
exists_wf,
map_append,
cons_wf,
map_cons_lemma,
map_nil_lemma,
general-append-cancellation,
length_of_cons_lemma,
length_of_nil_lemma,
hd_wf,
listp_properties,
list-cases,
cons_neq_nil,
product_subtype_list,
nat_wf,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
set_wf,
reduce_hd_cons_lemma,
tl_wf,
reduce_tl_cons_lemma
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)].
\mforall{}p,q:LocalClass(X).
p = q supposing \mforall{}i:Id. \mforall{}inputs:Info List. hdf-halted(p i*(inputs)) = hdf-halted(q i*(inputs))
Date html generated:
2015_07_21-PM-04_46_38
Last ObjectModification:
2015_02_04-PM-05_58_03
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