Nuprl Lemma : firstn-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:ℕ||(e1, e2)||]. (firstn(n;(e1, e2)) = (e1, (e1, e2)[n]) ∈ (E List))
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-E: E,
event_ordering: EO,
firstn: firstn(n;as),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
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,
iff: P ⇐⇒ Q,
l_member: (x ∈ l),
cand: A c∧ B,
gt: i > j,
true: True,
rev_implies: P ⇐ Q,
es-open-interval: (e, e'),
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\mBbbN{}||(e1, e2)||]. (firstn(n;(e1, e2)) = (e1, (e1, e2)[n]))
Date html generated:
2016_05_16-AM-09_36_50
Last ObjectModification:
2016_01_17-PM-01_28_33
Theory : new!event-ordering
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