Nuprl Lemma : es-interface-buffer-as-accum
∀[Info,A1:Type]. ∀[n:ℕ]. ∀[X:EClass(A1)].
(Buffer(n;X) = es-interface-accum(λL,v. if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;[];X) ∈ EClass(A1 List))
Proof
Definitions occuring in Statement :
es-interface-buffer: Buffer(n;X),
es-interface-accum: es-interface-accum(f;x;X),
eclass: EClass(A[eo; e]),
length: ||as||,
append: as @ bs,
tl: tl(l),
cons: [a / b],
nil: [],
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
uimplies: b supposing a,
sv-class: Singlevalued(X),
all: ∀x:A. B[x],
es-interface-accum: es-interface-accum(f;x;X),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
es-interface-buffer: Buffer(n;X),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
es-E-interface: E(X),
true: True,
eclass-vals: X(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}[Info,A1:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:EClass(A1)].
(Buffer(n;X) = es-interface-accum(\mlambda{}L,v. if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;[];X))
Date html generated:
2016_05_17-AM-08_13_15
Last ObjectModification:
2016_01_17-PM-02_39_45
Theory : event-ordering
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