Nuprl Lemma : loc-on-path-cons
∀es:EO. ∀L:E List. ∀e:E. ∀i:Id. (loc-on-path(es;i;[e / L]) ⇐⇒ (loc(e) = i ∈ Id) ∨ loc-on-path(es;i;L))
Proof
Definitions occuring in Statement :
loc-on-path: loc-on-path(es;i;L),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
equal: s = t ∈ T
Lemmas :
list_ind_cons_lemma,
list_ind_nil_lemma,
or_wf,
loc-on-path_wf,
cons_wf,
nil_wf,
loc-on-path-append,
append_wf,
iff_wf,
Id_wf,
es-E_wf,
list_wf,
event_ordering_wf,
map_cons_lemma,
map_nil_lemma,
member_singleton,
es-loc_wf
\mforall{}es:EO. \mforall{}L:E List. \mforall{}e:E. \mforall{}i:Id. (loc-on-path(es;i;[e / L]) \mLeftarrow{}{}\mRightarrow{} (loc(e) = i) \mvee{} loc-on-path(es;i;L))
Date html generated:
2015_07_17-AM-08_52_40
Last ObjectModification:
2015_01_27-PM-01_17_33
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