Nuprl Lemma : filter-interface-predecessors-lower-bound-implies
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀P:E(X) ─→ 𝔹. ∀n:ℕ. ∀e:E.
∃f:ℕn ─→ {e':E(X)| (↑P[e']) ∧ e' ≤loc e } . ∀i,j:ℕn. (f i <loc f j) supposing i < j
supposing n ≤ ||filter(λe.P[e];≤(X)(e))||
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
filter: filter(P;l),
length: ||as||,
int_seg: {i..j-},
nat: ℕ,
assert: ↑b,
bool: 𝔹,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
natural_number: $n,
universe: Type
Lemmas :
less_than_wf,
length_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
Id_wf,
es-loc_wf,
filter_wf5,
es-interface-predecessors_wf,
l_member_wf,
set_wf,
le_wf,
nat_wf,
bool_wf,
eclass_wf,
sorted-by-filter,
es-locl_wf,
es-interface-predecessors-sorted-by-locl,
filter_type,
int_seg_wf,
assert_wf,
sorted-by_wf,
all_wf,
es-le_wf,
select_wf,
sq_stable__le,
less_than_transitivity1,
select_member,
subtype_rel_list,
lelt_wf,
member_filter,
member-interface-predecessors2,
isect_wf,
equal_wf,
sq_stable__assert
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}P:E(X) {}\mrightarrow{} \mBbbB{}. \mforall{}n:\mBbbN{}. \mforall{}e:E.
\mexists{}f:\mBbbN{}n {}\mrightarrow{} \{e':E(X)| (\muparrow{}P[e']) \mwedge{} e' \mleq{}loc e \} . \mforall{}i,j:\mBbbN{}n. (f i <loc f j) supposing i < j
supposing n \mleq{} ||filter(\mlambda{}e.P[e];\mleq{}(X)(e))||
Date html generated:
2015_07_21-PM-03_40_37
Last ObjectModification:
2015_01_27-PM-06_36_28
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