Nuprl Lemma : es-bound-list2
∀es:EO
∀[T:Type]
∀i:Id
∀[P:T ─→ ℙ]
∀L:T List
∀[Q:E ─→ {x:T| (x ∈ L)} ─→ ℙ]
((∀x:T. Dec(P[x]))
⇒ (∀x∈L.P[x] ⇒ (∃e:E. Q[e;x]))
⇒ ∃e'@i.True supposing ¬(∃x∈L. P[x])
⇒ ∃e'@i.(∀x∈L.P[x] ⇒ (∃e:E. (e ≤loc e' ∧ Q[e;x])))
supposing (∀x∈L.∀e:E. (Q[e;x] ⇒ (loc(e) = i ∈ Id))))
Proof
Definitions occuring in Statement :
existse-at: ∃e@i.P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
l_exists: (∃x∈L. P[x]),
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
list: T List,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
true: True,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
select_wf,
l_member_wf,
list-subtype,
sq_stable__le,
es-E_wf,
int_seg_wf,
length_wf,
list-set-type,
es-bound-list,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
isect_wf,
not_wf,
l_exists_wf,
existse-at_wf,
es-loc_wf,
true_wf,
l_all_wf2,
exists_wf,
all_wf,
decidable_wf,
list_wf,
Id_wf,
event_ordering_wf
\mforall{}es:EO
\mforall{}[T:Type]
\mforall{}i:Id
\mforall{}[P:T {}\mrightarrow{} \mBbbP{}]
\mforall{}L:T List
\mforall{}[Q:E {}\mrightarrow{} \{x:T| (x \mmember{} L)\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}x:T. Dec(P[x]))
{}\mRightarrow{} (\mforall{}x\mmember{}L.P[x] {}\mRightarrow{} (\mexists{}e:E. Q[e;x]))
{}\mRightarrow{} \mexists{}e'@i.True supposing \mneg{}(\mexists{}x\mmember{}L. P[x])
{}\mRightarrow{} \mexists{}e'@i.(\mforall{}x\mmember{}L.P[x] {}\mRightarrow{} (\mexists{}e:E. (e \mleq{}loc e' \mwedge{} Q[e;x])))
supposing (\mforall{}x\mmember{}L.\mforall{}e:E. (Q[e;x] {}\mRightarrow{} (loc(e) = i))))
Date html generated:
2015_07_17-AM-08_50_54
Last ObjectModification:
2015_01_27-PM-01_19_35
Home
Index