Nuprl Lemma : not_over_forall3
T:Type. P:T 
.
((R:. (
R 
(
R))) 
(((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 :
all: x:A. B[x],
prop: ,
implies: P Q,
squash: T,
not: A,
and: P Q,
true: True,
member: t 
T,
so_lambda: 
x.t[x],
false: False,
exists: x:A. B[x],
uall: [x:A]. B[x],
so_apply: x[s],
or: P Q,
guard: {T}
Lemmas :
not_wf,
squash_wf,
all_wf,
exists_wf,
or_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{}(P t)))) \mwedge{} ((\mexists{}t:T. (\mneg{}(P t))) {}\mRightarrow{} (\mneg{}\mdownarrow{}\mforall{}t:T. (P t)))))
Date html generated:
2013_03_20-AM-10_49_12
Last ObjectModification:
2013_02_25-PM-07_20_49
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