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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-search-back: es-search-back(es;x.f[x];e),
gensearch: gensearch(f;g;x),
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
isl: isl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
es-pred?: es-pred?(es;e),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\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:
2016_05_16-AM-09_29_39
Last ObjectModification:
2015_12_28-PM-09_49_39
Theory : new!event-ordering
Home
Index