Nuprl Lemma : es-search-back-cases
∀[es:EO]. ∀[e:E]. ∀[f:{e':E| e' ≤loc e } ─→ (Top + Top)].
(es-search-back(es;x.f[x];e) ~ if isl(f[e]) then f[e]
if first(e) then inr ⋅
else es-search-back(es;x.f[x];pred(e))
fi )
Proof
Definitions occuring in Statement :
es-search-back: es-search-back(es;x.f[x];e),
es-le: e ≤loc e' ,
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
ifthenelse: if b then t else f fi ,
isl: isl(x),
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
inr: inr x ,
union: left + right,
sqequal: s ~ t
Lemmas :
es-le-self,
es-le_wf,
top_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-E_wf,
event_ordering_wf
\mforall{}[es:EO]. \mforall{}[e:E]. \mforall{}[f:\{e':E| e' \mleq{}loc e \} {}\mrightarrow{} (Top + Top)].
(es-search-back(es;x.f[x];e) \msim{} if isl(f[e]) then f[e]
if first(e) then inr \mcdot{}
else es-search-back(es;x.f[x];pred(e))
fi )
Date html generated:
2015_07_17-AM-08_40_13
Last ObjectModification:
2015_01_27-PM-02_40_31
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