{ norm-combinator-def() 
id-fun(CombinatorDef) }
{ Proof }
Definitions occuring in Statement :
norm-combinator-def: norm-combinator-def(),
combinator-def: CombinatorDef,
member: t T,
id-fun: id-fun(T)
Definitions :
length: ||as||,
int: 
,
equal: s = t,
universe: Type,
list: type List,
set: {x:A| B[x]} ,
squash: 
T,
nat: 
,
all: 
x:A. B[x],
tactic: Error :tactic,
RepeatFor: Error :RepeatFor,
D: Error :D,
cons: [car / cdr],
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
nil: [],
MaAuto: Error :MaAuto,
prop: 
,
label: ...$L... t,
not: 
A,
false: False,
true: True,
bool: 
,
tl: tl(l),
hd: hd(l),
strong-subtype: strong-subtype(A;B),
fpf: a:A fp-> B[a],
subtype_rel: A 
r B,
pair: <a, b>,
eclass: EClass(A[eo; e]),
product: x:A 
B[x],
implies: P 
Q,
ndlist: ndlist(T),
listp: A List
,
add: n + m,
minus: -n,
ge: i 
j ,
le: A 
B,
subtype: S T,
top: Top,
isect: 
x:A. B[x],
void: Void,
function: x:A 
B[x],
subtract: n - m,
natural_number: $n,
less_than: a < b,
member: t T,
decision: Decision,
inl: inl x ,
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
valueall-type: valueall-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
es-E-interface: E(X),
atom: Atom$n,
atom: Atom,
rec: rec(x.A[x]),
tunion: 
x:A.B[x],
b-union: A B,
in-eclass: e 
X,
eq_knd: a = b,
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,
bnot: b,
unit: Unit,
intensional-universe: IType,
so_apply: x[s],
or: P Q,
guard: {T},
l_member: (x l),
assert: 
b,
value-type: value-type(T),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
empty-bag: {},
uiff: uiff(P;Q),
union: left + right,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
rationals: 
,
lelt: i j < k,
cand: A c B,
real: 
,
grp_car: |g|,
lambda: 
x.A[x],
and: P Q,
int_seg: {i..j
},
select: l[i],
apply: f a,
bag: bag(T),
ifthenelse: if b then t else f fi ,
so_lambda: 
x.t[x],
id-fun: id-fun(T),
sq-id-fun: sq-id-fun(T),
uimplies: b supposing a,
uall: [x:A]. B[x],
norm-pair: norm-pair(Na;Nb),
combinator-def: CombinatorDef,
norm-combinator-def: norm-combinator-def()
Lemmas :
bag_wf,
ifthenelse_wf,
int_seg_properties,
select_wf,
int_seg_wf,
bool_wf,
norm-pair_wf,
permutation_wf,
empty-bag_wf,
subtype_rel_wf,
value-type_wf,
id-fun_wf,
intensional-universe_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
le_wf,
set-value-type,
int-value-type,
product-value-type,
sq_stable__value-type,
unit_wf,
union-value-type,
sq_stable__all,
function-value-type,
false_wf,
length_wf1,
top_wf,
member_wf,
length_wf_nat,
non_neg_length,
length_cons,
length_wf2,
length_nil,
nat_ind_tp,
nat_wf,
squash_wf,
nat_properties,
ge_wf
norm-combinator-def() \mmember{} id-fun(CombinatorDef)
Date html generated:
2011_08_17-PM-04_30_07
Last ObjectModification:
2011_06_18-AM-11_41_51
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