Nuprl Lemma : bind-df-next2_wf
[M,A,B,S:Type]. [F:S 
M (S? 
bag(A))]. [dfpY:A DataflowProgram(M)]. [m:M].
[s:S? bag(a:A df-program-statetype(dfpY a))].
bind-df-next2(F;dfpY;s;m) 
S? bag(a:A df-program-statetype(dfpY a))? bag(B)
supposing a:A. (df-program-type(dfpY a) 
r B)
Proof not projected
Definitions occuring in Statement :
bind-df-next2: bind-df-next2(F;dfpY;s;m),
df-program-statetype: df-program-statetype(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
unit: Unit,
member: t T,
apply: f a,
function: x:A B[x],
product: x:A B[x],
union: left + right,
universe: Type,
bag: bag(T)
Definitions :
so_apply: x[s],
true: True,
squash: 
T,
and: P 
Q,
prop: 
,
subtype: S T,
top: Top,
so_lambda: 
x.t[x],
implies: P 
Q,
bfalse: ff,
btrue: tt,
pi2: snd(t),
let: let,
outl: outl(x),
isl: isl(x),
ifthenelse: if b then t else f fi ,
bind-df-next2: bind-df-next2(F;dfpY;s;m),
member: t T,
all: x:A. B[x],
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T}
Lemmas :
true_wf,
squash_wf,
bool_wf,
equal_wf,
and_wf,
dataflow-program_wf,
df-program-type_wf,
subtype_rel_wf,
all_wf,
outl_wf,
assert_wf,
top_wf,
pi1_wf_top,
isl_wf,
bag-mapfilter_wf,
pi2_wf,
bag-combine_wf,
unit_wf2,
bag_wf,
bind-nextouts2_wf,
df-program-statetype_wf,
df-program-state_wf,
bag-map_wf,
bag-append_wf,
empty-bag_wf
\mforall{}[M,A,B,S:Type]. \mforall{}[F:S {}\mrightarrow{} M {}\mrightarrow{} (S? \mtimes{} bag(A))]. \mforall{}[dfpY:A {}\mrightarrow{} DataflowProgram(M)]. \mforall{}[m:M].
\mforall{}[s:S? \mtimes{} bag(a:A \mtimes{} df-program-statetype(dfpY a))].
bind-df-next2(F;dfpY;s;m) \mmember{} S? \mtimes{} bag(a:A \mtimes{} df-program-statetype(dfpY a))? \mtimes{} bag(B)
supposing \mforall{}a:A. (df-program-type(dfpY a) \msubseteq{}r B)
Date html generated:
2012_01_23-PM-12_01_55
Last ObjectModification:
2011_12_17-PM-12_40_41
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