{ 
[A,C:Type]. [B:A 
Type].
[eq:EqDecider(A)]. [f,g:x:A fp-> B[x] List]. [R:C List C 
].
(fpf-union-compatible(A;C;x.B[x];eq;R;f;g) 
)
supposing x:A. (B[x] 
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],
prop: ,
so_apply: x[s],
all: x:A. B[x],
member: t T,
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],
member: t T,
prop: ,
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
implies: P 
Q,
or: P 
Q,
and: P 
Q,
exists: 
x:A. B[x],
cand: A c B,
so_lambda: 
x.t[x],
subtype: S T,
rev_implies: P 
Q,
rev_uimplies: rev_uimplies(P;Q),
rev_subtype_rel: A 
r B,
l_member: (x l),
guard: {T}
Lemmas :
assert_wf,
fpf-dom_wf,
l_member_wf,
fpf-ap_wf,
implies_weakening_uimplies,
subtype_rel_wf,
subtype_rel_functionality_wrt_implies,
subtype_rel_weakening,
ext-eq_inversion,
ext-eq_weakening,
not_wf,
bool_wf,
fpf_wf,
deq_wf
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}[eq:EqDecider(A)]. \mforall{}[f,g: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;g) \mmember{} \mBbbP{})
supposing \mforall{}x:A. (B[x] \msubseteq{}r C)
Date html generated:
2011_08_10-AM-07_56_11
Last ObjectModification:
2011_06_18-AM-08_17_05
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