{ 
[A:Type]. [B:A 
Type]. [eq:EqDecider(A)]. [f1,g,f2:a:A fp-> B[a]].
(f1 
f2 
g) supposing (f2 g and f1 g) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-sub: f g,
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
guard: {T},
sq_type: SQType(T),
subtype: S T,
l_member: (x 
l),
list: type List,
top: Top,
bool: 
,
fpf-empty: 
,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
set: {x:A| B[x]} ,
subtype_rel: A r B,
fpf-join: f g,
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 ,
assert: 
b,
product: x:A 
B[x],
cand: A c B,
implies: P 
Q,
prop: 
,
fpf-sub: f g,
uimplies: b supposing a,
lambda: 
x.A[x],
all: x:A. B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
so_lambda: 
x.t[x],
so_apply: x[s],
apply: f a,
member: t T,
equal: s = t,
universe: Type,
deq: EqDecider(T),
function: x:A B[x],
Repeat: Error :Repeat,
MaAuto: Error :MaAuto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
rev_implies: P 
Q,
iff: P Q,
fpf-compatible: f || g
Lemmas :
subtype_rel_wf,
fpf-compatible_wf,
iff_wf,
rev_implies_wf,
fpf-join-idempotent,
fpf-join-sub,
member_wf,
fpf_wf,
top_wf,
l_member_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
assert_wf,
fpf-sub_wf,
assert_witness,
pair_wf,
deq_wf,
fpf-join_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f1,g,f2:a:A fp-> B[a]].
(f1 \moplus{} f2 \msubseteq{} g) supposing (f2 \msubseteq{} g and f1 \msubseteq{} g)
Date html generated:
2011_08_10-AM-08_00_47
Last ObjectModification:
2011_06_18-AM-08_19_38
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