Nuprl Lemma : not_over_forall_exists
T1,T2:Type. P:T1 
T2 
.
((R:. (
R 
(
R))) 
(t1:T1. (
t2:T2. (P t1 t2))) (t1:T1. (t2:T2. (P t1 t2))))
Proof
Definitions occuring in Statement :
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
squash: T,
implies: P Q,
or: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
all: x:A. B[x],
prop: ,
implies: P Q,
squash: T,
true: True,
member: t 
T,
so_lambda: 
x.t[x],
exists: x:A. B[x],
not: A,
so_apply: x[s],
false: False,
uall: [x:A]. B[x],
uiff: uiff(P;Q),
and: P 
Q,
uimplies: b supposing a
Lemmas :
not_wf,
squash_wf,
all_wf,
exists_wf,
or_wf,
not_over_forall4,
not_over_exists
\mforall{}T1,T2:Type. \mforall{}P:T1 {}\mrightarrow{} T2 {}\mrightarrow{} \mBbbP{}.
((\mforall{}R:\mBbbP{}. (\mdownarrow{}R \mvee{} (\mneg{}R))) {}\mRightarrow{} (\mneg{}\mdownarrow{}\mforall{}t1:T1. (\mdownarrow{}\mexists{}t2:T2. (\mdownarrow{}P t1 t2))) {}\mRightarrow{} (\mdownarrow{}\mexists{}t1:T1. (\mdownarrow{}\mforall{}t2:T2. (\mneg{}\mdownarrow{}P t1 t2))))
Date html generated:
2013_03_20-AM-10_49_26
Last ObjectModification:
2013_02_25-PM-08_40_45
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