Nuprl Lemma : State-loc-comb-classrel-non-loc
∀[Info,B,A:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
  ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.  ∀[v:B]. (v ∈ State-loc-comb(init;f;X)(e) 
⇐⇒ v ∈ State-comb(init;f loc(e);X)(e))
Proof
Definitions occuring in Statement : 
State-loc-comb: State-loc-comb(init;f;X)
, 
State-comb: State-comb(init;f;X)
, 
classrel: v ∈ X(e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-loc: loc(e)
, 
es-E: E
, 
Id: Id
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
bag: bag(T)
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
strongwellfounded: SWellFounded(R[x; y])
, 
exists: ∃x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
, 
squash: ↓T
, 
rev_implies: P 
⇐ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
less_than: a < b
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
uiff: uiff(P;Q)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
State-loc-comb: State-loc-comb(init;f;X)
, 
simple-loc-comb-2: F o (Loc,X, Y)
, 
simple-loc-comb: F|Loc; Xs|
, 
select: L[n]
, 
cons: [a / b]
, 
subtract: n - m
, 
eclass: EClass(A[eo; e])
, 
State-comb: State-comb(init;f;X)
, 
simple-comb-2: F|X, Y|
, 
simple-comb: simple-comb(F;Xs)
, 
sq_type: SQType(T)
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
bfalse: ff
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
rev_uimplies: rev_uimplies(P;Q)
, 
cand: A c∧ B
, 
so_lambda: λ2x.t[x]
, 
bnot: ¬bb
, 
assert: ↑b
, 
so_apply: x[s]
, 
es-p-local-pred: es-p-local-pred(es;P)
, 
lifting-loc-2: lifting-loc-2(f)
, 
lifting2-loc: lifting2-loc(f;loc;abag;bbag)
, 
lifting-loc-gen-rev: lifting-loc-gen-rev(n;bags;loc;f)
, 
lifting-gen-rev: lifting-gen-rev(n;f;bags)
, 
lifting-gen-list-rev: lifting-gen-list-rev(n;bags)
, 
eq_int: (i =z j)
, 
lifting-2: lifting-2(f)
, 
lifting2: lifting2(f;abag;bbag)
, 
es-locl: (e <loc e')
, 
sq_stable: SqStable(P)
Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
    \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.
        \mforall{}[v:B].  (v  \mmember{}  State-loc-comb(init;f;X)(e)  \mLeftarrow{}{}\mRightarrow{}  v  \mmember{}  State-comb(init;f  loc(e);X)(e))
Date html generated:
2016_05_17-AM-10_01_17
Last ObjectModification:
2016_01_17-PM-11_13_25
Theory : classrel!lemmas
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