Nuprl Lemma : pi-guarded-trans_wf
∀[compList:(pi_prefix() × pi_term()) List]. ∀[g:{Q:pi_term()| (∃C∈compList. pi-rank(Q) ≤ pi-rank(snd(C)))}
─→ Id
─→ Name
─→ (Name List)
─→ pi-process()].
(pi-guarded-trans(compList;g) ∈ Id ─→ Name ─→ (Name List) ─→ pi-process())
Proof
Definitions occuring in Statement :
pi-guarded-trans: pi-guarded-trans(compList;g),
pi-process: pi-process(),
pi-rank: pi-rank(p),
pi_term: pi_term(),
pi_prefix: pi_prefix(),
Id: Id,
name: Name,
l_exists: (∃x∈L. P[x]),
list: T List,
uall: ∀[x:A]. B[x],
pi2: snd(t),
le: A ≤ B,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
product: x:A × B[x]
Lemmas :
fix_wf_corec_3parameter,
piM_wf,
ldag_wf,
Id_wf,
Com_wf,
name_wf,
list_wf,
continuous-constant,
pDVfire?_wf,
bool_wf,
eqtt_to_assert,
make-lg_wf_dag,
cons_wf,
mk-tagged_wf_pCom_msg,
PiDataVal_wf,
subtype_rel_wf,
sq_stable__subtype_rel,
pDVfire_wf,
subtype_rel_self,
pi_prefix_wf,
nat_wf,
unit_wf2,
nil_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
Process_wf,
pi-guarded-aux_wf,
pi-process_wf,
subtype_rel_transitivity
Latex:
\mforall{}[compList:(pi\_prefix() \mtimes{} pi\_term()) List]. \mforall{}[g:\{Q:pi\_term()|
(\mexists{}C\mmember{}compList. pi-rank(Q) \mleq{} pi-rank(snd(C)))\}
{}\mrightarrow{} Id
{}\mrightarrow{} Name
{}\mrightarrow{} (Name List)
{}\mrightarrow{} pi-process()].
(pi-guarded-trans(compList;g) \mmember{} Id {}\mrightarrow{} Name {}\mrightarrow{} (Name List) {}\mrightarrow{} pi-process())
Date html generated:
2015_07_23-AM-11_59_27
Last ObjectModification:
2015_01_29-AM-07_46_30
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