Nuprl Lemma : isl-es-search-back
∀es:EO. ∀[T:Type]. ∀e:E. ∀f:{e':E| e' ≤loc e } ⟶ (T + Top). (↑isl(es-search-back(es;x.f[x];e)) ⇐⇒ ∃e'≤e.↑isl(f[e']))
Proof
Definitions occuring in Statement :
existse-le: ∃e≤e'.P[e],
es-search-back: es-search-back(es;x.f[x];e),
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
existse-le: ∃e≤e'.P[e],
member: t ∈ T,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
isl: isl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bfalse: ff,
sq_type: SQType(T),
true: True,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bnot: ¬bb,
es-le: e ≤loc e' ,
es-locl: (e <loc e')
Latex:
\mforall{}es:EO
\mforall{}[T:Type]
\mforall{}e:E. \mforall{}f:\{e':E| e' \mleq{}loc e \} {}\mrightarrow{} (T + Top).
(\muparrow{}isl(es-search-back(es;x.f[x];e)) \mLeftarrow{}{}\mRightarrow{} \mexists{}e'\mleq{}e.\muparrow{}isl(f[e']))
Date html generated:
2016_05_16-AM-09_46_47
Last ObjectModification:
2016_01_17-PM-01_27_35
Theory : new!event-ordering
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