Nuprl Lemma : last-event-of-set
∀es:EO. ∀n:ℕ+. ∀f:ℕn ─→ E. ∃k:ℕn. ∀i:ℕn. f i ≤loc f k supposing ∀i,j:ℕn. (loc(f i) = loc(f j) ∈ Id)
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
nat_plus: ℕ+,
int_seg: {i..j-},
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
equal: s = t ∈ T
Lemmas :
nat_plus_properties,
all_wf,
int_seg_wf,
es-E_wf,
isect_wf,
equal_wf,
Id_wf,
es-loc_wf,
exists_wf,
es-le_wf,
primrec-wf-nat-plus,
nat_plus_wf,
event_ordering_wf,
false_wf,
lelt_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
es-le-self,
not-equal-2,
sq_stable__le,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
less-iff-le,
le-add-cancel2,
subtype_rel_dep_function,
subtype_rel-int_seg,
decidable__le,
not-le-2,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
subtype_rel_self,
decidable__lt,
decidable__es-le,
le_weakening2,
and_wf,
decidable__es-locl,
es-le-not-locl,
es-locl_transitivity1,
es-le_weakening
\mforall{}es:EO. \mforall{}n:\mBbbN{}\msupplus{}. \mforall{}f:\mBbbN{}n {}\mrightarrow{} E. \mexists{}k:\mBbbN{}n. \mforall{}i:\mBbbN{}n. f i \mleq{}loc f k supposing \mforall{}i,j:\mBbbN{}n. (loc(f i) = loc(f j))
Date html generated:
2015_07_17-AM-08_39_51
Last ObjectModification:
2015_01_27-PM-02_43_52
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