Nuprl Lemma : decidable__exists-last-classrel-between3-sv
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info).
(single-valued-classrel(es;X;T)
⇒ (∀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 :
single-valued-classrel: single-valued-classrel(es;X;T),
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,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Lemmas :
decidable__exists-last-classrel-between3,
es-E_wf,
event-ordering+_subtype,
single-valued-classrel_wf,
event-ordering+_wf,
eclass_wf,
decidable__exists-single-valued-classrel,
es-locl_wf,
es-le_wf,
exists_wf,
classrel_wf,
all_wf,
not_wf,
squash_wf
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info).
(single-valued-classrel(es;X;T)
{}\mRightarrow{} (\mforall{}e1,e2:E.
Dec(\mexists{}e:E
((e1 <loc e)
\mwedge{} e \mleq{}loc e2
\mwedge{} (\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_22_44
Last ObjectModification:
2015_01_27-PM-11_37_47
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