Nuprl Lemma : es-search-back_wf
∀[es:EO]. ∀[T:Type]. ∀[e:E]. ∀[f:{e':E| e' ≤loc e } ⟶ (T + Top)]. (es-search-back(es;x.f[x];e) ∈ T + Top)
Proof
Definitions occuring in Statement :
es-search-back: es-search-back(es;x.f[x];e),
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-search-back: es-search-back(es;x.f[x];e),
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
so_lambda: λ2x.t[x],
cand: A c∧ B,
guard: {T},
top: Top,
isl: isl(x),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Latex:
\mforall{}[es:EO]. \mforall{}[T:Type]. \mforall{}[e:E]. \mforall{}[f:\{e':E| e' \mleq{}loc e \} {}\mrightarrow{} (T + Top)].
(es-search-back(es;x.f[x];e) \mmember{} T + Top)
Date html generated:
2016_05_16-AM-09_29_34
Last ObjectModification:
2015_12_28-PM-09_50_09
Theory : new!event-ordering
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