Nuprl Lemma : member-eclass-simple-loc-comb-2-iff
∀[Info,A,B,C:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[F:Id ⟶ bag(A) ⟶ bag(B) ⟶ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
  (uiff(↑e ∈b F o (Loc,X, Y);(↑e ∈b X) ∧ (↑e ∈b Y) ∧ (¬↑bag-null(F loc(e) {X@e} {Y@e})))) supposing 
     (single-valued-classrel(es;Y;B) and 
     single-valued-classrel(es;X;A) and 
     lifting2-like(A;B;F loc(e)))
Proof
Definitions occuring in Statement : 
lifting2-like: lifting2-like(A;B;f)
, 
simple-loc-comb-2: F o (Loc,X, Y)
, 
classfun-res: X@e
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
member-eclass: e ∈b X
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-loc: loc(e)
, 
es-E: E
, 
Id: Id
, 
assert: ↑b
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
and: P ∧ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
bag-null: bag-null(bs)
, 
single-bag: {x}
, 
bag: bag(T)
Definitions unfolded in proof : 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
false: False
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
lifting2-like: lifting2-like(A;B;f)
, 
simple-loc-comb-2: F o (Loc,X, Y)
, 
member-eclass: e ∈b X
, 
simple-loc-comb: F|Loc; Xs|
, 
select: L[n]
, 
cons: [a / b]
, 
subtract: n - m
, 
eclass: EClass(A[eo; e])
, 
nat: ℕ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
cand: A c∧ B
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
classrel: v ∈ X(e)
, 
single-valued-bag: single-valued-bag(b;T)
, 
guard: {T}
, 
rev_uimplies: rev_uimplies(P;Q)
, 
nequal: a ≠ b ∈ T 
Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[F:Id  {}\mrightarrow{}  bag(A)  {}\mrightarrow{}  bag(B)  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)].
    (uiff(\muparrow{}e  \mmember{}\msubb{}  F  o  (Loc,X,  Y);(\muparrow{}e  \mmember{}\msubb{}  X)  \mwedge{}  (\muparrow{}e  \mmember{}\msubb{}  Y)  \mwedge{}  (\mneg{}\muparrow{}bag-null(F  loc(e)  \{X@e\}  \{Y@e\}))))  supposing 
          (single-valued-classrel(es;Y;B)  and 
          single-valued-classrel(es;X;A)  and 
          lifting2-like(A;B;F  loc(e)))
Date html generated:
2016_05_17-AM-11_14_36
Last ObjectModification:
2016_01_18-AM-00_11_34
Theory : process-model
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