Nuprl Lemma : nth_tl-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:ℕ||(e1, e2)||].
nth_tl(n + 1;(e1, e2)) = ((e1, e2)[n], e2) ∈ (E List) supposing loc(e1) = loc(e2) ∈ Id
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
select: L[n],
length: ||as||,
nth_tl: nth_tl(n;as),
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
subtract: n - m,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
select: L[n],
cons: [a / b],
uiff: uiff(P;Q),
true: True,
l_member: (x ∈ l),
es-locl: (e <loc e')
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\mBbbN{}||(e1, e2)||].
nth\_tl(n + 1;(e1, e2)) = ((e1, e2)[n], e2) supposing loc(e1) = loc(e2)
Date html generated:
2016_05_16-AM-09_37_24
Last ObjectModification:
2016_01_17-PM-01_29_24
Theory : new!event-ordering
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