{ 
[A:Type]. [B:A 
Type]. [C: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)
fpf-union-compatible(A;C;x.B[x];eq;R;g;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],
implies: P Q,
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],
implies: P Q,
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
member: t 
T,
so_lambda: 
x.t[x],
or: P 
Q,
and: P 
Q,
prop: 
,
subtype: S T,
cand: A c B,
guard: {T},
rev_implies: P 
Q,
rev_uimplies: rev_uimplies(P;Q),
rev_subtype_rel: A 
r B,
exists: 
x:A. B[x],
l_member: (x l)
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf-union-compatible_wf,
bool_wf,
fpf_wf,
deq_wf,
l_member_wf,
fpf-ap_wf,
not_wf,
implies_weakening_uimplies,
subtype_rel_wf,
subtype_rel_functionality_wrt_implies,
subtype_rel_weakening,
ext-eq_inversion,
ext-eq_weakening
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[C: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) {}\mRightarrow{} fpf-union-compatible(A;C;x.B[x];eq;R;g;f))
supposing \mforall{}a:A. (B[a] \msubseteq{}r C)
Date html generated:
2011_08_10-AM-07_56_15
Last ObjectModification:
2011_06_18-AM-08_17_08
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