{ 
[A,C:Type]. [B:A 
Type].
eq:EqDecider(A). f:x:A fp-> B[x] List. R:C List C 
.
fpf-union-compatible(A;C;x.B[x];eq;R;f;f)
supposing a:A. (B[a] 
r C) }
{ Proof }
Definitions occuring in Statement :
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
fpf: a:A fp-> B[a],
subtype_rel: A r B,
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
function: x:A B[x],
list: type List,
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
all: x:A. B[x],
so_apply: x[s],
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
member: t 
T,
implies: P 
Q,
and: P 
Q,
not: 
A,
exists: 
x:A. B[x],
so_lambda: 
x.t[x],
cand: A c B,
le: A 
B,
false: False,
int_seg: {i..j
},
lelt: i j < k,
prop: 
,
or: P 
Q,
subtype: S T,
l_member: (x l),
nat: 
,
guard: {T}
Lemmas :
bool_wf,
fpf_wf,
deq_wf,
select_wf,
fpf-ap_wf,
nat_properties,
select_member,
le_wf,
length_wf1,
l_member_wf,
not_wf,
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f:x:A fp-> B[x] List. \mforall{}R:C List {}\mrightarrow{} C {}\mrightarrow{} \mBbbB{}.
fpf-union-compatible(A;C;x.B[x];eq;R;f;f)
supposing \mforall{}a:A. (B[a] \msubseteq{}r C)
Date html generated:
2011_08_10-AM-07_56_23
Last ObjectModification:
2011_06_18-AM-08_17_12
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