{ 
[a:Atom1]. [A:Type]. [eq:EqDecider(A)]. [B:A 
']. [f:x:A fp-> B[x]].
[x:A]. (f(x):B[x]||a) supposing ((
x 
dom(f)) and x:A||a)
supposing f:x:A fp-> B[x]||a }
{ Proof }
Definitions occuring in Statement :
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
deq: EqDecider(T),
free-from-atom: x:T||a,
atom: Atom$n
Definitions :
implies: P 
Q,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
fpf-ap: f(x),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
set: {x:A| B[x]} ,
list: type List,
product: x:A 
B[x],
subtype_rel: A 
r B,
top: Top,
fpf-dom: x dom(f),
assert: b,
prop: 
,
free-from-atom: x:T||a,
uimplies: b supposing a,
lambda: 
x.A[x],
apply: f a,
so_apply: x[s],
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
all: x:A. B[x],
isect: 
x:A. B[x],
deq: EqDecider(T),
atom: Atom$n,
equal: s = t,
function: x:A B[x],
member: t T,
uall: [x:A]. B[x],
Repeat: Error :Repeat,
Auto: Error :Auto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
universe: Type,
iff: P 
Q,
int: 
,
nat: 
,
exists: 
x:A. B[x],
fpf-domain: fpf-domain(f),
l_member: (x l),
void: Void,
subtype: S T,
pi1: fst(t),
pi2: snd(t),
pair: <a, b>,
guard: {T},
true: True,
squash: 
T,
sq_type: SQType(T),
sqequal: s ~ t
Lemmas :
set_subtype_base,
subtype_base_sq,
squash_wf,
true_wf,
pi2_wf,
pi1_wf_top,
l_member_wf,
fpf-domain_wf,
subtype_rel_wf,
member-fpf-domain,
deq_wf,
free-from-atom_wf1,
assert_wf,
fpf-dom_wf,
top_wf,
fpf_wf,
member_wf,
fpf-trivial-subtype-top
\mforall{}[a:Atom1]. \mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} \mBbbU{}']. \mforall{}[f:x:A fp-> B[x]].
\mforall{}[x:A]. (f(x):B[x]||a) supposing ((\muparrow{}x \mmember{} dom(f)) and x:A||a) supposing f:x:A fp-> B[x]||a
Date html generated:
2011_08_10-AM-08_13_23
Last ObjectModification:
2011_06_18-AM-08_29_13
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