{ 
[M:Type 
Type]
lvProcess(lp.M[lp]) 
r (process-Input(lp.M[lp])
(lvProcess(lp.M[lp]) 
process-Output(lp.M[lp])))
supposing A,B:Type. ((A r B) 
(M[A] r M[B])) }
{ Proof }
Definitions occuring in Statement :
process-Output: process-Output(lp.M[lp]),
process-Input: process-Input(lp.M[lp]),
lvProcess: lvProcess(lp.M[lp]),
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
all: x:A. B[x],
implies: P Q,
so_apply: x[s],
lvProcess: lvProcess(lp.M[lp]),
member: t 
T,
so_lambda: 
x.t[x],
nat: 
,
process-input: input(lp.M[lp];n),
process-input': process-input'(lp.M[lp];n),
process-Input: process-Input(lp.M[lp]),
process-Output: process-Output(lp.M[lp]),
ifthenelse: if b then t else f fi ,
top: Top,
prop: 
,
btrue: tt,
bfalse: ff,
ext-eq: A 
B,
and: P 
Q,
int_seg: {i..j
},
bool: 
,
lelt: i 
j < k,
unit: Unit,
iff: P 
Q,
it: 
Lemmas :
tunion_wf,
nat_wf,
lvprocess_wf,
process-Input_wf,
process-Output_wf,
process-ext-eq,
subtype_rel_function,
ifthenelse_wf,
le_int_wf,
top_wf,
Id_wf,
int_seg_wf,
le_wf,
subtype_rel_product,
subtype_rel_self,
nat_properties,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
subtype_rel_simple_product,
subtype_rel_list
\mforall{}[M:Type {}\mrightarrow{} Type]
lvProcess(lp.M[lp]) \msubseteq{}r (process-Input(lp.M[lp])
{}\mrightarrow{} (lvProcess(lp.M[lp]) \mtimes{} process-Output(lp.M[lp])))
supposing \mforall{}A,B:Type. ((A \msubseteq{}r B) {}\mRightarrow{} (M[A] \msubseteq{}r M[B]))
Date html generated:
2011_08_17-PM-06_38_18
Last ObjectModification:
2011_06_18-PM-12_02_36
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