Nuprl Lemma : in-simple-loc-comb-1-concat
∀[Info,A,B:Type]. ∀[f:Id ⟶ A ⟶ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
(Singlevalued(X) ⇒ (∀i:Id. ∀a:A. (#(f i a) ≤ 1)) ⇒ e ∈b f@(Loc, X) = e ∈b X ∧b (¬bbag-null(f loc(e) X(e))))
Proof
Definitions occuring in Statement :
concat-lifting-loc-1: f@,
simple-loc-comb-1: F(Loc, X),
sv-class: Singlevalued(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
band: p ∧b q,
bnot: ¬bb,
bool: 𝔹,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag-null: bag-null(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
sv-class: Singlevalued(X),
simple-loc-comb-1: F(Loc, X),
simple-loc-comb: F|Loc; Xs|,
select: L[n],
cons: [a / b],
concat-lifting-loc-1: f@,
concat-lifting1-loc: concat-lifting1-loc(f;bag;loc),
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
in-eclass: e ∈b X,
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T ,
not: ¬A,
eclass-val: X(e),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
rev_implies: P ⇐ Q,
decidable: Dec(P),
ge: i ≥ j ,
le: A ≤ B
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(Singlevalued(X)
{}\mRightarrow{} (\mforall{}i:Id. \mforall{}a:A. (\#(f i a) \mleq{} 1))
{}\mRightarrow{} e \mmember{}\msubb{} f@(Loc, X) = e \mmember{}\msubb{} X \mwedge{}\msubb{} (\mneg{}\msubb{}bag-null(f loc(e) X(e))))
Date html generated:
2016_05_17-AM-11_17_04
Last ObjectModification:
2016_01_18-AM-00_12_29
Theory : process-model
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