Nuprl Lemma : simple-loc-comb-3-concat-single-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B,C,D:Type]. ∀[F:Id ⟶ A ⟶ B ⟶ C ⟶ bag(D)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
∀[Z:EClass(C)].
  single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D) 
  supposing (∀i:Id. ∀a:A. ∀b:B. ∀c:C.  (#(F i a b c) ≤ 1))
  ∧ single-valued-classrel(es;X;A)
  ∧ single-valued-classrel(es;Y;B)
  ∧ single-valued-classrel(es;Z;C)
Proof
Definitions occuring in Statement : 
concat-lifting-loc-3: concat-lifting-loc-3(f)
, 
simple-loc-comb-3: F|Loc, X, Y, Z|
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
Id: Id
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
, 
universe: Type
, 
bag-size: #(bs)
, 
bag: bag(T)
Definitions unfolded in proof : 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
and: P ∧ Q
, 
simple-loc-comb-3: F|Loc, X, Y, Z|
, 
simple-loc-comb: F|Loc; Xs|
, 
select: L[n]
, 
cons: [a / b]
, 
subtract: n - m
, 
classrel: v ∈ X(e)
, 
concat-lifting-loc-3: concat-lifting-loc-3(f)
, 
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f)
, 
concat-lifting: concat-lifting(n;f;bags)
, 
concat-lifting-list: concat-lifting-list(n;bags)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
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])
, 
squash: ↓T
, 
exists: ∃x:A. B[x]
, 
nat: ℕ
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
le: A ≤ B
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
false: False
, 
not: ¬A
, 
top: Top
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
cand: A c∧ B
, 
bag-member: x ↓∈ bs
Latex:
\mforall{}[Info:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[A,B,C,D:Type].  \mforall{}[F:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  C  {}\mrightarrow{}  bag(D)].  \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)].  \mforall{}[Z:EClass(C)].
    single-valued-classrel(es;concat-lifting-loc-3(F)|Loc,  X,  Y,  Z|;D) 
    supposing  (\mforall{}i:Id.  \mforall{}a:A.  \mforall{}b:B.  \mforall{}c:C.    (\#(F  i  a  b  c)  \mleq{}  1))
    \mwedge{}  single-valued-classrel(es;X;A)
    \mwedge{}  single-valued-classrel(es;Y;B)
    \mwedge{}  single-valued-classrel(es;Z;C)
Date html generated:
2016_05_17-AM-09_28_55
Last ObjectModification:
2016_01_17-PM-11_10_21
Theory : classrel!lemmas
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