Nuprl Lemma : es-interval-select
∀[es:EO]. ∀[e',e:E]. ∀[i:ℕ].
firstn(i;[e, e']) = if (i =z 0) then [] else [e, pred([e, e'][i])] fi ∈ (E List) supposing i < ||[e, e']||
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-pred: pred(e),
es-E: E,
event_ordering: EO,
firstn: firstn(n;as),
select: L[n],
length: ||as||,
nil: [],
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
squash: ↓T,
sq_type: SQType(T),
subtype_rel: A ⊆r B,
trans: Trans(T;x,y.E[x; y]),
true: True
Latex:
\mforall{}[es:EO]. \mforall{}[e',e:E]. \mforall{}[i:\mBbbN{}].
firstn(i;[e, e']) = if (i =\msubz{} 0) then [] else [e, pred([e, e'][i])] fi supposing i < ||[e, e']||
Date html generated:
2016_05_16-AM-09_34_13
Last ObjectModification:
2016_01_17-PM-01_33_50
Theory : new!event-ordering
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