Nuprl Lemma : TR4a
[T:Type]. [P:T 
]. [C:].
((C 
(
C)) 
(
x:T. True) (((x:T. (P x))) (x:T. ((P x)))) ((x:T. (P x)) C) (x:T. ((P x) C)))
Proof
Definitions occuring in Statement :
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
or: P Q,
true: True,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
implies: P Q,
member: t 
T,
prop: ,
so_lambda: 
x.t[x],
all: x:A. B[x],
exists: x:A. B[x],
subtype_rel: A 
r B,
not: A,
uall: [x:A]. B[x],
so_apply: x[s],
or: P Q,
false: False
Lemmas :
all_wf,
not_wf,
exists_wf,
true_wf,
or_wf
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[C:\mBbbP{}].
((C \mvee{} (\mneg{}C))
{}\mRightarrow{} (\mexists{}x:T. True)
{}\mRightarrow{} ((\mneg{}(\mforall{}x:T. (P x))) {}\mRightarrow{} (\mexists{}x:T. (\mneg{}(P x))))
{}\mRightarrow{} ((\mforall{}x:T. (P x)) {}\mRightarrow{} C)
{}\mRightarrow{} (\mexists{}x:T. ((P x) {}\mRightarrow{} C)))
Date html generated:
2014_07_17-AM-09_55_38
Last ObjectModification:
2014_06_18-PM-01_42_02
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