Nuprl Lemma : Comm-process-q_aux_wf
∀[q:(Id × (pi_prefix() List)) List]
(Comm-process-q_aux(q) ∈ Id
─→ st:Id fp-> pi_prefix() List
─→ ((Id × (pi_prefix() List)) List × st:Id fp-> pi_prefix() List × Id × ((ℕ × Id × ℕ × Name) List)))
Proof
Definitions occuring in Statement :
Comm-process-q_aux: Comm-process-q_aux(q),
pi_prefix: pi_prefix(),
fpf: a:A fp-> B[a],
Id: Id,
name: Name,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x]
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
Id_wf,
list_wf,
pi_prefix_wf,
list-cases,
list_ind_nil_lemma,
nil_wf,
name_wf,
fpf_wf,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
list_ind_cons_lemma,
let_wf,
null_nil_lemma,
null_cons_lemma,
cons_wf,
get-triples_wf,
fpf-join_wf,
fpf-single_wf,
id-deq_wf
Latex:
\mforall{}[q:(Id \mtimes{} (pi\_prefix() List)) List]
(Comm-process-q\_aux(q) \mmember{} Id
{}\mrightarrow{} st:Id fp-> pi\_prefix() List
{}\mrightarrow{} ((Id \mtimes{} (pi\_prefix() List)) List
\mtimes{} st:Id fp-> pi\_prefix() List
\mtimes{} Id
\mtimes{} ((\mBbbN{} \mtimes{} Id \mtimes{} \mBbbN{} \mtimes{} Name) List)))
Date html generated:
2015_07_23-AM-11_58_46
Last ObjectModification:
2015_01_29-AM-07_40_57
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