Nuprl Lemma : not_over_forall4
T:Type. P:T 
. ((R:. (
R 
(
R))) 
(t:T. (P t)) (
t:T. (P t)))
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],
not: A,
exists: x:A. B[x],
uall: [x:A]. B[x],
so_apply: x[s],
or: P Q,
false: False
Lemmas :
not_wf,
squash_wf,
all_wf,
or_wf,
exists_wf
\mforall{}T:Type. \mforall{}P:T {}\mrightarrow{} \mBbbP{}. ((\mforall{}R:\mBbbP{}. (\mdownarrow{}R \mvee{} (\mneg{}R))) {}\mRightarrow{} (\mneg{}\mdownarrow{}\mforall{}t:T. (\mdownarrow{}P t)) {}\mRightarrow{} (\mdownarrow{}\mexists{}t:T. (\mneg{}\mdownarrow{}P t)))
Date html generated:
2013_03_20-AM-10_49_16
Last ObjectModification:
2013_02_25-PM-07_39_35
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