Nuprl Lemma : nth_tl-es-before
∀[es:EO]. ∀[e:E]. ∀[n:ℕ||before(e)||]. (nth_tl(n;before(e)) = filter(λa.before(e)[n] ≤loc a;before(e)) ∈ (E List))
Proof
Definitions occuring in Statement :
es-before: before(e),
es-ble: e ≤loc e',
es-E: E,
event_ordering: EO,
select: L[n],
length: ||as||,
filter: filter(P;l),
nth_tl: nth_tl(n;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
select: L[n],
cons: [a / b],
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}||before(e)||].
(nth\_tl(n;before(e)) = filter(\mlambda{}a.before(e)[n] \mleq{}loc a;before(e)))
Date html generated:
2016_05_16-AM-09_35_49
Last ObjectModification:
2016_01_17-PM-01_32_42
Theory : new!event-ordering
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