{ 
[M:Type 
Type]
[m:
]. (lvprocess(lp.M[lp];m) 
r lvprocess(lp.M[lp];m + 1))
supposing A,B:Type. ((A r B) 
(M[A] r M[B])) }
{ Proof }
Definitions occuring in Statement :
lvprocess: lvprocess(lp.M[lp];n),
subtype_rel: A r B,
nat: ,
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],
add: n + m,
natural_number: $n,
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];n),
member: t 
T,
ycomb: Y,
process-input': process-input'(lp.M[lp];n),
process-input: input(lp.M[lp];n),
nat: ,
dataflow: dataflow(A;B),
type-monotone: Monotone(T.F[T]),
so_lambda: 
x.t[x],
le: A 
B,
not: 
A,
false: False,
ifthenelse: if b then t else f fi ,
top: Top,
btrue: tt,
prop: 
,
and: P 
Q,
bfalse: ff,
int_seg: {i..j
},
lelt: i j < k,
ext-eq: A 
B,
bool: 
,
unit: Unit,
iff: P 
Q,
it: 
Lemmas :
nat_wf,
subtype-corec,
process-input_wf,
le_wf,
Id_wf,
process-input'_wf,
subtype_rel_function,
subtype_rel_simple_product,
lvprocess_wf,
subtype_rel_transitivity,
process-ext-eq,
subtype_rel_product,
subtype_rel_self,
le_int_wf,
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,
top_wf,
subtype_rel_list,
int_seg_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[m:\mBbbN{}]. (lvprocess(lp.M[lp];m) \msubseteq{}r lvprocess(lp.M[lp];m + 1))
supposing \mforall{}A,B:Type. ((A \msubseteq{}r B) {}\mRightarrow{} (M[A] \msubseteq{}r M[B]))
Date html generated:
2011_08_17-PM-06_37_31
Last ObjectModification:
2011_06_18-PM-12_01_22
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