Nuprl Lemma : loc-on-path-decomp
∀[Info:Type]
∀es:EO+(Info). ∀Sys:EClass(Top). ∀L:E(Sys) List. ∀j:Id.
(loc-on-path(es;j;L)
⇒ (∃u:E(Sys)
∃A,B:E(Sys) List. ((loc(u) = j ∈ Id) ∧ (L = (A @ [u / B]) ∈ (E(Sys) List)) ∧ (¬loc-on-path(es;j;A)))))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
loc-on-path: loc-on-path(es;i;L),
es-loc: loc(e),
Id: Id,
append: as @ bs,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_induction,
all_wf,
Id_wf,
loc-on-path_wf,
event-ordering+_subtype,
subtype_rel_list,
es-E_wf,
exists_wf,
es-loc_wf,
append_wf,
cons_wf,
length_wf,
length-append,
not_wf,
list_wf,
es-E-interface_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
nil_wf,
loc-on-path-nil,
loc-on-path-cons,
decidable__equal_Id,
list_ind_nil_lemma,
length_of_cons_lemma,
nil-append,
list_ind_cons_lemma,
true_wf,
squash_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}Sys:EClass(Top). \mforall{}L:E(Sys) List. \mforall{}j:Id.
(loc-on-path(es;j;L)
{}\mRightarrow{} (\mexists{}u:E(Sys). \mexists{}A,B:E(Sys) List. ((loc(u) = j) \mwedge{} (L = (A @ [u / B])) \mwedge{} (\mneg{}loc-on-path(es;j;A)))))
Date html generated:
2015_07_17-PM-01_01_49
Last ObjectModification:
2015_07_16-AM-09_43_29
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