{ 
[M:Type 
Type]
[n,m:
]. input(lp.M[lp];n) 
r input(lp.M[lp];m) supposing m 
n
supposing A,B:Type. ((A r B) 
(M[A] r M[B])) }
{ Proof }
Definitions occuring in Statement :
process-input: input(lp.M[lp];n),
subtype_rel: A r B,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
le: A B,
all: x:A. B[x],
implies: P Q,
function: 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],
process-input: input(lp.M[lp];n),
member: t 
T,
ifthenelse: if b then t else f fi ,
top: Top,
so_lambda: 
x.t[x],
btrue: tt,
prop: 
,
bfalse: ff,
nat: ,
le: A B,
bool: 
,
unit: Unit,
iff: P 
Q,
and: P 
Q,
not: 
A,
false: False,
it: 
Lemmas :
subtype_rel_product,
subtype_rel_self,
le_int_wf,
nat_properties,
bool_wf,
iff_weakening_uiff,
le_wf,
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,
lvprocess_wf,
top_wf,
nat_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[n,m:\mBbbN{}]. input(lp.M[lp];n) \msubseteq{}r input(lp.M[lp];m) supposing m \mleq{} n
supposing \mforall{}A,B:Type. ((A \msubseteq{}r B) {}\mRightarrow{} (M[A] \msubseteq{}r M[B]))
Date html generated:
2011_08_17-PM-06_36_33
Last ObjectModification:
2011_06_18-AM-11_59_52
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