Nuprl Lemma : parallel-as-bind
∀[A,Info:Type]. ∀[X,Y:EClass(A)]. (X || Y = return-bag-class(tt.ff.{}) >b> if b then X else Y fi ∈ EClass(A))
Proof
Definitions occuring in Statement :
return-bag-class: return-bag-class(b),
parallel-class: X || Y,
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T,
cons-bag: x.b,
empty-bag: {}
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
return-bag-class: return-bag-class(b),
bind-class: X >x> Y[x],
parallel-class: X || Y,
eclass: EClass(A[eo; e]),
all: ∀x:A. B[x],
top: Top,
eclass-compose2: eclass-compose2(f;X;Y),
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
true: True,
so_apply: x[s],
uimplies: b supposing a,
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
single-bag: {x},
cons-bag: x.b,
bag-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
bag-union: bag-union(bbs),
concat: concat(ll),
bag-append: as + bs,
empty-bag: {},
class-ap: X(e),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cons: [a / b],
not: ¬A,
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
subtract: n - m,
less_than': less_than'(a;b),
listp: A List+,
ge: i ≥ j ,
bag-null: bag-null(bs),
null: null(as),
nil: []
Latex:
\mforall{}[A,Info:Type]. \mforall{}[X,Y:EClass(A)]. (X || Y = return-bag-class(tt.ff.\{\}) >b> if b then X else Y fi )
Date html generated:
2016_05_16-PM-02_31_36
Last ObjectModification:
2016_05_12-PM-05_34_52
Theory : event-ordering
Home
Index