{ 
[A:Type]. [B1,B2:A 
Type]. [eq:EqDecider(A)]. [f:a:A fp-> B1[a]].
[g:a:A fp-> B2[a]].
f 
f 
g }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-sub: f g,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
or: P 
Q,
rev_implies: P 
Q,
iff: P 
Q,
list: type List,
top: Top,
strong-subtype: strong-subtype(A;B),
set: {x:A| B[x]} ,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
fpf-ap: f(x),
fpf-join: f g,
fpf-dom: x 
dom(f),
prop: 
,
axiom: Ax,
pair: <a, b>,
lambda: 
x.A[x],
fpf-sub: f g,
all: x:A. B[x],
implies: P Q,
cand: A c B,
product: x:A 
B[x],
assert: 
b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
false: False,
void: Void,
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,
isect: 
x:A. B[x],
fpf: a:A fp-> B[a],
member: t T,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
tactic: Error :tactic
Lemmas :
top_wf,
member_wf,
fpf_wf,
fpf-join_wf,
fpf-dom_wf,
assert_wf,
fpf-trivial-subtype-top,
subtype_rel_wf,
fpf-ap_wf,
true_wf,
ifthenelse_wf,
false_wf,
assert_witness,
pair_wf,
deq_wf,
fpf-join-dom2,
iff_wf,
rev_implies_wf,
fpf-join-ap-left
\mforall{}[A:Type]. \mforall{}[B1,B2:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f:a:A fp-> B1[a]]. \mforall{}[g:a:A fp-> B2[a]].
f \msubseteq{} f \moplus{} g
Date html generated:
2011_08_10-AM-08_00_14
Last ObjectModification:
2011_06_18-AM-08_19_23
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