{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [f:a:A fp-> B[a]]. [x:A].
[v:B[x]].
uiff(f || x : v;v = f(x) supposing 
x 
dom(f)) }
{ Proof }
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
so_apply: x[s],
uiff: uiff(P;Q),
fpf-compatible: f || g,
uimplies: b supposing a,
member: t T,
and: P 
Q,
prop: 
,
top: Top,
so_lambda: 
x.t[x],
all: x:A. B[x],
implies: P 
Q,
fpf-ap: f(x),
fpf-single: x : v,
pi2: snd(t),
squash: 
T,
true: True,
rev_implies: P 
Q,
iff: P Q
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf-compatible_wf,
fpf-single_wf,
top_wf,
fpf-ap_wf,
fpf_wf,
deq_wf,
eqof_wf,
fpf-single-dom-sq,
iff_weakening_uiff,
uiff_inversion,
deq_property,
squash_wf,
true_wf,
bool_wf,
member_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[v:B[x]].
uiff(f || x : v;v = f(x) supposing \muparrow{}x \mmember{} dom(f))
Date html generated:
2011_08_10-AM-08_06_37
Last ObjectModification:
2011_06_18-AM-08_24_55
Home
Index