Nuprl Lemma : not_over_forall
(
P:
. (
P 
(
P)))
(T:Type. P:T 
. ((((t:T. (P t))) (
t:T. ((P t)))) 
((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,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
false: False,
so_lambda: 
x.t[x],
member: t 
T,
true: True,
and: P Q,
not: A,
squash: T,
prop: ,
all: x:A. B[x],
implies: P Q,
exists: x:A. B[x],
so_apply: x[s],
uall: [x:A]. B[x],
or: P Q,
guard: {T}
Lemmas :
or_wf,
exists_wf,
squash_wf,
all_wf,
not_wf
(\mforall{}P:\mBbbP{}. (\mdownarrow{}P \mvee{} (\mneg{}P)))
{}\mRightarrow{} (\mforall{}T:Type. \mforall{}P:T {}\mrightarrow{} \mBbbP{}.
(((\mneg{}(\mforall{}t:T. (\mdownarrow{}P t))) {}\mRightarrow{} (\mdownarrow{}\mexists{}t:T. (\mneg{}(P t)))) \mwedge{} ((\mexists{}t:T. (\mneg{}(P t))) {}\mRightarrow{} (\mneg{}(\mforall{}t:T. (P t))))))
Date html generated:
2013_03_20-AM-10_49_03
Last ObjectModification:
2013_02_25-PM-04_58_32
Home
Index