Nuprl Lemma : not_over_forall_exists_form
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,
not: A,
false: False,
member: t 
T,
so_lambda: 
x.t[x],
squash: T,
exists: x:A. B[x],
true: True,
uall: [x:A]. B[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P 
Q,
uimplies: b supposing a,
iff: P 
Q
Lemmas :
squash_wf,
all_wf,
exists_wf,
not_wf,
or_wf,
not_over_forall_form_squash,
not_over_exists,
not_squash_elim
\mforall{}T1,T2:Type. \mforall{}P:T1 {}\mrightarrow{} T2 {}\mrightarrow{} \mBbbP{}.
((\mforall{}R:\mBbbP{}. (\mdownarrow{}R \mvee{} (\mneg{}R))) {}\mRightarrow{} (\mdownarrow{}\mexists{}t1:T1. (\mdownarrow{}\mforall{}t2:T2. (\mneg{}\mdownarrow{}P t1 t2))) {}\mRightarrow{} (\mneg{}\mdownarrow{}\mforall{}t1:T1. (\mdownarrow{}\mexists{}t2:T2. (\mdownarrow{}P t1 t2))))
Date html generated:
2013_03_20-AM-10_49_32
Last ObjectModification:
2013_02_25-PM-10_23_50
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