{ 
[A:Type]. [B:A 
Type]. [eq:EqDecider(A)]. [f,g:a:A fp-> B[a]].
(f 
g 
(
x,y.<Ax, Ax> 
f g)) }
{ Proof }
Definitions occuring in Statement :
fpf-sub: f g,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s],
implies: P Q,
member: t T,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
universe: Type,
axiom: Ax,
deq: EqDecider(T)
Definitions :
guard: {T},
sq_type: SQType(T),
subtype: S T,
l_member: (x l),
list: type List,
top: Top,
bool: 
,
fpf-ap: f(x),
fpf-dom: x dom(f),
cand: A c
B,
strong-subtype: strong-subtype(A;B),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
set: {x:A| B[x]} ,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
prop: 
,
axiom: Ax,
pair: <a, b>,
fpf-sub: f g,
lambda: x.A[x],
implies: P Q,
equal: s = t,
universe: Type,
function: x:A B[x],
deq: EqDecider(T),
uall: [x:A]. B[x],
so_lambda: 
x.t[x],
so_apply: x[s],
apply: f a,
fpf: a:A fp-> B[a],
member: t T,
isect: 
x:A. B[x],
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
tactic: Error :tactic
Lemmas :
fpf_wf,
top_wf,
member_wf,
l_member_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
assert_wf,
assert_witness,
pair_wf,
deq_wf,
fpf-sub_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> B[a]].
(f \msubseteq{} g {}\mRightarrow{} (\mlambda{}x,y.<Ax, Ax> \mmember{} f \msubseteq{} g))
Date html generated:
2011_08_10-AM-07_56_46
Last ObjectModification:
2011_06_18-AM-08_17_22
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