{ 
[X:Type]. [eq:EqDecider(X)]. [f,g:x:X fp-> Type]. [x:X].
(f(x)?Void List) 
r (g(x)?Void List) supposing f g }
{ Proof }
Definitions occuring in Statement :
fpf-sub: f g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
list: type List,
void: Void,
universe: Type,
deq: EqDecider(T)
Definitions :
member: t 
T,
so_lambda: 
x.t[x],
prop: 
,
uall: [x:A]. B[x],
uimplies: b supposing a,
fpf-cap: f(x)?z,
all: x:A. B[x],
subtype: S T,
implies: P 
Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_apply: x[s],
fpf-sub: f g,
or: P 
Q,
sq_type: SQType(T),
guard: {T},
iff: P 
Q,
and: P 
Q,
cand: A c B,
not: 
A,
false: False,
bool: 
,
unit: Unit,
it: 
Lemmas :
fpf-dom_wf,
fpf-trivial-subtype-top,
bool_wf,
assert_wf,
not_wf,
bnot_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-cap_wf,
fpf-sub_wf,
fpf_wf,
deq_wf,
fpf-ap_wf
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[f,g:x:X fp-> Type]. \mforall{}[x:X].
(f(x)?Void List) \msubseteq{}r (g(x)?Void List) supposing f \msubseteq{} g
Date html generated:
2011_08_10-AM-07_58_42
Last ObjectModification:
2011_06_18-AM-08_18_33
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