Nuprl Lemma : es-first-at-exists
∀es:EO. ∀i:Id.
∀[P:{e:E| loc(e) = i ∈ Id} ─→ ℙ]
((∀e:{e:E| loc(e) = i ∈ Id} . Dec(P[e]))
⇒ (∀e:E. P[e] ⇒ (∃e':E. (e' ≤loc e ∧ e' is first@ i s.t. e.P[e])) supposing loc(e) = i ∈ Id))
Proof
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
decidable__existse-before,
subtype_rel_dep_function,
es-E_wf,
Id_wf,
es-loc_wf,
subtype_rel_sets,
equal_wf,
subtype_rel_self,
set_wf,
es-causl_weakening,
es-locl_transitivity1,
es-le_weakening,
es-le_wf,
es-first-at_wf,
es-le-self,
es-locl_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:\{e:E| loc(e) = i\} . Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. P[e] {}\mRightarrow{} (\mexists{}e':E. (e' \mleq{}loc e \mwedge{} e' is first@ i s.t. e.P[e])) supposing loc(e) = i))
Date html generated:
2015_07_17-AM-08_50_03
Last ObjectModification:
2015_01_27-PM-02_29_01
Home
Index