{ 
[A:Type]. [P:A 
]. [B:A Type]. [eq:EqDecider(A)].
[f,g:a:{a:A| P[a]} fp-> B[a]].
f 
g supposing f g }
{ Proof }
Definitions occuring in Statement :
fpf-sub: f g,
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
suptype: suptype(S; T),
rev_implies: P 
Q,
iff: P 
Q,
eq_knd: a = b,
fpf-domain: fpf-domain(f),
intensional-universe: IType,
sq_type: SQType(T),
subtype: S T,
fpf-empty: 
,
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
union: left + right,
or: P 
Q,
guard: {T},
l_member: (x 
l),
bool: 
,
top: Top,
fpf-ap: f(x),
fpf-dom: x dom(f),
axiom: Ax,
pair: <a, b>,
void: Void,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
cand: A c
B,
implies: P Q,
strong-subtype: strong-subtype(A;B),
list: type List,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P Q,
uiff: uiff(P;Q),
assert: 
b,
product: x:A 
B[x],
subtype_rel: A r B,
fpf-sub: f g,
uimplies: b supposing a,
lambda: 
x.A[x],
set: {x:A| B[x]} ,
apply: f a,
so_apply: x[s],
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
isect: 
x:A. B[x],
all: x:A. B[x],
prop: ,
uall: [x:A]. B[x],
deq: EqDecider(T),
function: x:A B[x],
member: t T,
equal: s = t,
universe: Type,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
cons: [car / cdr],
nil: [],
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
bor: p 
q,
band: p q,
bimplies: p q,
bnot: b,
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
natural_number: $n,
int: 
,
length: ||as||,
exists: 
x:A. B[x],
nat: 
,
select: l[i],
squash: 
T
Lemmas :
deq-member_wf,
select_wf,
nat_properties,
assert-deq-member,
subtype_rel_wf,
fpf_wf,
top_wf,
fpf-trivial-subtype-top,
member_wf,
fpf-dom_wf,
assert_wf,
fpf-sub_wf,
assert_witness,
pair_wf,
deq_wf,
l_member_wf,
intensional-universe_wf,
fpf-type,
subtype-fpf3,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
iff_wf,
bool_wf,
fpf-ap_wf,
strong-subtype-deq-subtype
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:\{a:A| P[a]\} fp-> B[a]].
f \msubseteq{} g supposing f \msubseteq{} g
Date html generated:
2011_08_10-AM-07_56_56
Last ObjectModification:
2010_11_10-PM-02_33_08
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