Nuprl Lemma : exists_over_implies_pull
T:Type. P:
. Q:T 
. (T 
Dec(P) (P (
x:T. (Q x))) (x:T. (P (Q x))))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
all: x:A. B[x],
prop: ,
implies: P Q,
exists: x:A. B[x],
member: t 
T,
so_lambda: 
x.t[x],
uall: [x:A]. B[x],
so_apply: x[s],
decidable: Dec(P),
or: P 
Q,
not: 
A,
false: False
Lemmas :
exists_wf,
decidable_wf
\mforall{}T:Type. \mforall{}P:\mBbbP{}. \mforall{}Q:T {}\mrightarrow{} \mBbbP{}. (T {}\mRightarrow{} Dec(P) {}\mRightarrow{} (P {}\mRightarrow{} (\mexists{}x:T. (Q x))) {}\mRightarrow{} (\mexists{}x:T. (P {}\mRightarrow{} (Q x))))
Date html generated:
2013_03_20-AM-09_45_13
Last ObjectModification:
2013_03_12-PM-06_24_16
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