Nuprl Lemma : pRun_functionality
∀[M:Type ─→ Type]
∀[nat2msg:ℕ ─→ pMsg(P.M[P])]. ∀[loc2msg:Id ─→ pMsg(P.M[P])]. ∀[env:pEnvType(P.M[P])]. ∀[S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg) ∈ pRunType(P.M[P]) supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
nat_properties,
nequal-le-implies,
zero-add,
all_wf,
system-equiv_wf,
pRun_wf,
fulpRunType_wf,
int_seg_subtype-nat,
Id_wf,
pMsg_wf,
unit_wf2,
System_wf,
top_wf,
ldag_wf,
pInTransit_wf,
subtype_rel_product,
list_wf,
component_wf,
subtype_rel_self,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
lelt_wf,
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
it_wf,
system-equiv-implies-equal,
subtract-is-less,
lg-is-source_wf,
assert_elim,
and_wf,
not_assert_elim,
btrue_neq_bfalse,
lg-remove_wf_dag,
squash_wf,
true_wf,
lg-label_wf,
lg-size_wf,
labeled-graph_wf,
lt_int_wf,
assert_wf,
bnot_wf,
not_wf,
bfalse_wf,
bool_cases,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
pCom_wf,
atom2_subtype_base,
atom_subtype_base,
com-kind_wf,
eq_atom_wf,
assert_of_eq_atom,
comm-msg_wf,
neg_assert_of_eq_atom,
deliver-msg_functionality,
equal-wf-T-base,
deliver-msg_wf,
length_of_cons_lemma,
int_subtype_base,
comm-create_wf,
Process_wf,
Process-stream_wf,
select_cons_tl,
minus-zero,
length_wf,
le-add-cancel2,
le_antisymmetry_iff,
process-equiv_wf,
iff_weakening_equal,
do-chosen-command_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[nat2msg:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[loc2msg:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[env:pEnvType(P.M[P])].
\mforall{}[S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg)
supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_10_03
Last ObjectModification:
2015_02_04-PM-04_51_50
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