Nuprl Lemma : pRun-invariant1
∀[M:Type ─→ Type]
∀n2m:ℕ ─→ pMsg(P.M[P]). ∀l2m:Id ─→ pMsg(P.M[P]). ∀S0:System(P.M[P]). ∀env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
∀e:runEvents(r)
(fst(fst(run-info(r;e))) < run-event-step(e)
∨ (∃m:ℕlg-size(snd(S0)). ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))) ∈ (ℤ × Id))))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
pRun-intransit-invariant,
nat_wf,
pRun_wf2,
decidable__assert,
is-run-event_wf,
sq_stable__assert,
runEvents_wf,
pEnvType_wf,
System_wf,
Id_wf,
pMsg_wf,
strong-type-continuous_wf,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
assert_of_lt_int,
bool_cases,
less_than_wf,
not_wf,
bnot_wf,
assert_wf,
lelt_wf,
lg-label_wf,
lg-size_wf,
lt_int_wf,
pInTransit_wf,
lg-is-source_wf,
le-add-cancel,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul,
condition-implies-le,
sq_stable__le,
not-le-2,
decidable__le,
pRun_wf,
zero-add,
nequal-le-implies,
nat_properties,
le_wf,
int_upper_subtype_nat,
neg_assert_of_eq_int,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
false_wf,
assert_of_eq_int,
eqtt_to_assert,
bool_wf,
eq_int_wf,
subtract_wf,
lg-all_wf,
eq_id_wf,
le-add-cancel-alt,
pCom_wf,
subtype_top,
top_wf,
subtype_rel_product,
pi1_wf_top,
labeled-graph_wf,
true_wf,
squash_wf,
atom2_subtype_base,
int_subtype_base,
product_subtype_base,
is-dag_wf,
pi2_wf,
ldag_wf,
component_wf,
list_wf,
and_wf,
or_wf,
less-iff-le,
int_seg_wf,
exists_wf,
decidable__lt,
unit_wf2,
fulpRunType_wf,
neg_assert_of_eq_atom,
assert_of_eq_atom,
com-kind_wf,
eq_atom_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}S0:System(P.M[P]). \mforall{}env:pEnvType(P.M[P]).
let r = pRun(S0;env;n2m;l2m) in
\mforall{}e:runEvents(r)
(fst(fst(run-info(r;e))) < run-event-step(e)
\mvee{} (\mexists{}m:\mBbbN{}lg-size(snd(S0)). ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))))))
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_14_25
Last ObjectModification:
2015_07_16-AM-09_38_53
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