Nuprl Lemma : int_enumerability_nat
T:Type. ((
f:
T. Surj(;T;f)) 
(g:
T. Surj(;T;g)))
Proof
Definitions occuring in Statement :
surject: Surj(A;B;f),
nat: ,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
function: x:A B[x],
int: ,
universe: Type
Definitions :
all: x:A. B[x],
implies: P Q,
member: t 
T,
so_lambda: 
x.t[x],
exists: x:A. B[x],
nat: ,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
surject: Surj(A;B;f),
int_nzero: 
,
nequal: a 
b T ,
not: 
A,
false: False,
and: P 
Q,
prop: 
,
iff: P 
Q,
rev_implies: P Q,
nat_plus: 
,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
guard: {T},
le: A 
B,
sq_type: SQType(T),
it: 
Lemmas :
surject_wf,
nat_wf,
exists_wf,
bool_wf,
uiff_transitivity,
equal_wf,
subtype_rel_weakening,
ext-eq_weakening,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
le_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
div_rem_sum,
nequal_wf,
ifthenelse_wf,
eq_int_wf,
assert_of_eq_int,
lt_int_wf,
iff_transitivity,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
subtype_base_sq,
int_subtype_base,
rem_bounds_1,
div_bounds_1
\mforall{}T:Type. ((\mexists{}f:\mBbbN{} {}\mrightarrow{} T. Surj(\mBbbN{};T;f)) {}\mRightarrow{} (\mexists{}g:\mBbbZ{} {}\mrightarrow{} T. Surj(\mBbbZ{};T;g)))
Date html generated:
2013_03_20-AM-09_49_46
Last ObjectModification:
2012_11_27-AM-10_32_05
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