Nuprl Lemma : decidable__exists-last-classrel-between3
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e1,e2:E.
Dec(∃e:E
((e1 <loc e)
∧ e ≤loc e2
∧ (↓∃v:T. v ∈ X(e))
∧ (∀e'':E. ((e <loc e'') ⇒ e'' ≤loc e2 ⇒ (∀x:T. (¬x ∈ X(e'')))))))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Lemmas :
event-ordering+_subtype,
es-locl-trichotomy,
add-zero,
zero-mul,
add-mul-special,
le_wf,
zero-le-nat,
primrec-wf2,
set_wf,
not_wf,
classrel_wf,
squash_wf,
es-le_wf,
exists_wf,
decidable_wf,
nat_wf,
all_wf,
es-loc_wf,
Id_wf,
equal_wf,
es-locl_wf,
decidable__exists_classrel,
es-causl_wf,
le-add-cancel,
add-associates,
add_functionality_wrt_le,
less-iff-le,
add-commutes,
add-swap,
minus-one-mul,
minus-minus,
minus-add,
condition-implies-le,
false_wf,
subtract_wf,
decidable__lt,
es-E_wf,
less_than_wf,
es-causl-swellfnd,
es-locl_irreflexivity,
es-locl_transitivity2,
es-le-self,
iff_weakening_equal,
es-pred-loc-base,
es-first_wf2,
assert_wf,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
es-pred_wf,
es-pred-causl,
and_wf,
es-le-pred,
es-locl_transitivity1,
es-pred-locl,
bool_subtype_base,
subtype_base_sq,
es-causl_irreflexivity,
es-causle_wf,
es-causle_weakening_eq,
es-causle_weakening,
es-causl_transitivity2,
es-le_weakening_eq,
es-causl_weakening,
es-loc-pred,
es-pred_property,
es-le_weakening,
es-le-loc
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e1,e2:E.
Dec(\mexists{}e:E
((e1 <loc e)
\mwedge{} e \mleq{}loc e2
\mwedge{} (\mdownarrow{}\mexists{}v:T. v \mmember{} X(e))
\mwedge{} (\mforall{}e'':E. ((e <loc e'') {}\mRightarrow{} e'' \mleq{}loc e2 {}\mRightarrow{} (\mforall{}x:T. (\mneg{}x \mmember{} X(e'')))))))
Date html generated:
2015_07_17-PM-00_18_29
Last ObjectModification:
2015_07_16-AM-09_44_08
Home
Index