{ 
[env:E#Env]. [F:Atom]. [r:{dv:ClassDerivation|
WF(dv) 
(||cdv-types(dv)|| = 1)} List].
esharp-comb(env;
F;r) 
{dv:ClassDerivation| WF(dv) (||cdv-types(dv)|| = 1)}
supposing esharp-comb-wf(env;F;r) }
{ Proof }
Definitions occuring in Statement :
esharp-comb: esharp-comb,
esharp-comb-wf: esharp-comb-wf(env;F;ra),
esharp-env: E#Env,
cdv-wf: WF(dv),
cdv-types: cdv-types(dv),
classderiv: ClassDerivation,
length: ||as||,
uimplies: b supposing a,
uall: [x:A]. B[x],
and: P Q,
member: t T,
set: {x:A| B[x]} ,
list: type List,
natural_number: $n,
int: 
,
atom: Atom,
equal: s = t
Definitions :
lelt: i 
j < k,
limited-type: LimitedType,
sqequal: s ~ t,
rec: rec(x.A[x]),
pi2: snd(t),
ycomb: Y,
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
so_apply: x[s],
or: P 
Q,
guard: {T},
pi1: fst(t),
filter: filter(P;l),
l_member: (x l),
intensional-universe: IType,
void: Void,
assert: 
b,
listp: A List
,
combination: Combination(n;T),
real: 
,
grp_car: |g|,
cand: A c B,
empty-bag: {},
pair: <a, b>,
bool: 
,
nat: 
,
spread: spread def,
classderiv_ind: classderiv_ind,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
name: Name,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
inl: inl x ,
map: map(f;as),
bag: bag(T),
pack-cdv-args: pack-cdv-args(n;m;L),
cdvcomb: cdvcomb(typ;argtype;arg;fun),
cdvreccomb: cdvreccomb(typ;argtype;arg;fun),
let: let,
spreadn: spread6,
nil: [],
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
atom-deq: AtomDeq,
implies: P 
Q,
unit: Unit,
combinator-def: CombinatorDef,
base-deriv: BaseDef,
apply-alist: apply-alist(eq;L;x),
hd: hd(l),
subtype: S T,
all: x:A. B[x],
axiom: Ax,
esharp-comb: esharp-comb,
cdv-types: cdv-types(dv),
esharp-comb-wf: esharp-comb-wf(env;F;ra),
prop: 
,
list: type List,
and: P Q,
product: x:A 
B[x],
cdv-wf: WF(dv),
classderiv: ClassDerivation,
atom: Atom,
esharp-env: E#Env,
uall: [x:A]. B[x],
so_lambda: 
x.t[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
top: Top,
select: l[i],
union: left + right,
length: ||as||,
natural_number: $n,
int_seg: {i..j
},
function: x:A 
B[x],
universe: Type,
it: 
,
inr: inr x ,
lambda: x.A[x],
apply: f a,
equal: s = t,
ifthenelse: if b then t else f fi ,
set: {x:A| B[x]} ,
member: t T,
add: n + m,
int: ,
in-eclass: e 
X,
eq_knd: a = b,
bfalse: ff,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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,
bnot: b,
btrue: tt,
sq_type: SQType(T),
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
true: True,
squash: 
T,
eqof: eqof(d),
fpf-dom: x dom(f),
rcv: rcv(l,tg),
locl: locl(a),
ext-eq: A 
B,
class-program: ClassProgram(T),
es-E-interface: E(X),
fpf-cap: f(x)?z,
THENL_cons: Error :THENL_nil,
D: Error :D,
Unfold: Error :Unfold,
AssertBY: Error :AssertBY,
THENL_v2: Error :THENL,
THENL_cons: Error :THENL_cons,
MaAuto: Error :MaAuto,
Try: Error :Try,
Complete: Error :Complete,
RepeatFor: Error :RepeatFor,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
SplitOn: Error :SplitOn,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
cdv-argtype: cdv-argtype(dv),
l_all: (xL.P[x]),
rev_implies: P 
Q,
iff: P Q,
limited-type-level: limited-type-level{i:l}(n;T),
atom: Atom$n,
base: Base,
exists: x:A. B[x],
cdvcomb-typ: cdvcomb-typ(x),
cdvcomb-argtype: cdvcomb-argtype(x),
cdvcomb-arg: cdvcomb-arg(x),
classderiv_ind_cdvcomb: classderiv_ind_cdvcomb_compseq_tag_def,
cdvcomb-fun: cdvcomb-fun(x),
cdvbase?: cdvbase?(x),
cdvpair?: cdvpair?(x),
cdvdelay?: cdvdelay?(x),
cdvcomb?: cdvcomb?(x),
cdvreccomb?: cdvreccomb?(x),
cdvreccomb-typ: cdvreccomb-typ(x),
cdvreccomb-argtype: cdvreccomb-argtype(x),
cdvreccomb-arg: cdvreccomb-arg(x),
classderiv_ind_cdvreccomb: classderiv_ind_cdvreccomb_compseq_tag_def,
cdvreccomb-fun: cdvreccomb-fun(x),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v])
Lemmas :
cdvreccomb_wf,
cdvcomb_wf,
int_seg_properties,
cdv-argtype_wf,
limited-type-level_wf,
limited-type_wf,
product_subtype_base,
atom2_subtype_base,
Id_wf,
atom_subtype_base,
name_wf,
union_subtype_base,
base_wf,
rec_subtype_base,
set_subtype_base,
intensional-universe_subtype_base,
unit_subtype_base,
iff_wf,
rev_implies_wf,
cdv-argtype-pack,
l_all_wf,
pack-cdv-args_wf,
nat_wf,
list_subtype_base,
ifthenelse_wf,
ext-eq_weakening,
subtype_rel_weakening,
ext-eq_inversion,
empty-bag_wf,
bool_wf,
true_wf,
squash_wf,
permutation_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
subtype_rel_self,
classderiv_wf,
cdv-wf_wf,
uall_wf,
esharp-comb-wf_wf,
member_wf,
esharp-env_wf,
cdv-types_wf,
length_wf1,
base-deriv_wf,
combinator-def_wf,
apply-alist_wf,
unit_wf,
atom-deq_wf,
false_wf,
nat_properties,
hd_wf,
map_wf_listp,
listp_wf,
length_wf_nat,
map_wf,
subtype_rel_wf,
intensional-universe_wf,
list-subtype,
l_member_wf,
non_neg_length,
map_length,
ge_wf,
le_wf,
not_wf,
pos_length3,
top_wf,
length-map,
cdv-types-non-empty,
select_wf,
bag_wf,
int_seg_wf
\mforall{}[env:E\#Env]. \mforall{}[F:Atom]. \mforall{}[r:\{dv:ClassDerivation| WF(dv) \mwedge{} (||cdv-types(dv)|| = 1)\} List].
esharp-comb(env;
F;r) \mmember{} \{dv:ClassDerivation| WF(dv) \mwedge{} (||cdv-types(dv)|| = 1)\}
supposing esharp-comb-wf(env;F;r)
Date html generated:
2011_08_17-PM-04_33_11
Last ObjectModification:
2011_06_18-AM-11_43_54
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