{ 
[T:Type]. [P:T 
].
((x:T. Dec(P[x])) 
finite-type(T) Dec(
x:T. P[x])) }
{ Proof }
Definitions occuring in Statement :
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
function: x:A B[x],
universe: Type,
finite-type: finite-type(T)
Definitions :
uall: [x:A]. B[x],
prop: ,
implies: P Q,
all: x:A. B[x],
so_apply: x[s],
member: t 
T,
iff: P 
Q,
exists: x:A. B[x],
and: P 
Q,
rev_implies: P Q,
so_lambda: 
x.t[x],
finite-type: finite-type(T),
nat: 
,
surject: Surj(A;B;f)
Lemmas :
finite-type_wf,
decidable_wf,
int_seg_wf,
decidable_functionality,
decidable__ex_int_seg
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. Dec(P[x])) {}\mRightarrow{} finite-type(T) {}\mRightarrow{} Dec(\mexists{}x:T. P[x]))
Date html generated:
2011_08_16-AM-11_10_48
Last ObjectModification:
2011_06_20-AM-00_18_56
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