{ 
[P1,P2:Type 
']. [F:{T:Type| P1[T]} {T:Type| P2[T]} Type].
[H:
T1:{T:Type| P1[T]} . T2:{T:Type| P2[T]} .
{f:bag(T1) bag(T2) bag(F[T1;T2])| (f {} {}) = {}} ].
(SimpleComb2(T1.P1[T1];T2.P2[T2];T1,T2.F[T1;T2];a,b.H[a;b])
CombinatorDef) }
{ Proof }
Definitions occuring in Statement :
SimpleComb2: SimpleComb2(T1.P1[T1];T2.P2[T2];T1,T2.F[T1; T2];a,b.H[a; b]),
combinator-def: CombinatorDef,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
apply: f a,
isect: x:A. B[x],
function: x:A B[x],
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T)
Definitions :
es-E-interface: E(X),
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
in-eclass: e 
X,
or: P 
Q,
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p 
q,
bor: p q,
assert: 
b,
bnot: 
b,
unit: Unit,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
intensional-universe: IType,
union: left + right,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
lelt: i j < k,
nil: [],
cand: A c B,
grp_car: |g|,
p-outcome: Outcome,
void: Void,
implies: P Q,
false: False,
real: 
,
rationals: 
,
subtype: S 
T,
pair: <a, b>,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
axiom: Ax,
SimpleComb2: SimpleComb2(T1.P1[T1];T2.P2[T2];T1,T2.F[T1; T2];a,b.H[a; b]),
empty-bag: {},
lambda: 
x.A[x],
ifthenelse: if b then t else f fi ,
select: l[i],
int_seg: {i..j
},
and: P Q,
length: ||as||,
int: 
,
list: type List,
bool: 
,
add: n + m,
natural_number: $n,
less_than: a < b,
nat: 
,
product: x:A 
B[x],
so_apply: x[s1;s2],
combinator-def: CombinatorDef,
prop: ,
so_apply: x[s],
apply: f a,
universe: Type,
function: x:A B[x],
uall: [x:A]. B[x],
member: t T,
isect: x:A. B[x],
set: {x:A| B[x]} ,
equal: s = t,
bag: bag(T),
sq_type: SQType(T)
Lemmas :
subtype_base_sq,
int_subtype_base,
bag_wf,
ifthenelse_wf,
empty-bag_wf,
nat_wf,
bool_wf,
int_seg_wf,
select_wf,
member_wf,
le_wf,
not_wf,
false_wf,
nat_properties,
length_wf1,
int_seg_properties,
permutation_wf,
intensional-universe_wf,
subtype_rel_wf,
length_wf_nat,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
bfalse_wf,
pos_length2
\mforall{}[P1,P2:Type {}\mrightarrow{} \mBbbP{}']. \mforall{}[F:\{T:Type| P1[T]\} {}\mrightarrow{} \{T:Type| P2[T]\} {}\mrightarrow{} Type].
\mforall{}[H:\mcap{}T1:\{T:Type| P1[T]\} . \mcap{}T2:\{T:Type| P2[T]\} .
\{f:bag(T1) {}\mrightarrow{} bag(T2) {}\mrightarrow{} bag(F[T1;T2])| (f \{\} \{\}) = \{\}\} ].
(SimpleComb2(T1.P1[T1];T2.P2[T2];T1,T2.F[T1;T2];a,b.H[a;b]) \mmember{} CombinatorDef)
Date html generated:
2011_08_17-PM-04_30_43
Last ObjectModification:
2011_06_18-AM-11_42_15
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