Nuprl Lemma : TR8b
[T:Type]. [P:T 
]. [C:]. ((
x:T. True) 
(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],
implies: P Q,
and: P Q,
true: True,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
member: t 
T,
prop: ,
implies: P Q,
so_lambda: 
x.t[x],
and: P Q,
subtype_rel: A 
r B,
all: x:A. B[x],
so_apply: x[s],
exists: x:A. B[x]
Lemmas :
all_wf,
exists_wf,
true_wf
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[C:\mBbbP{}]. ((\mexists{}x:T. True) {}\mRightarrow{} (\mforall{}x:T. ((P x) \mwedge{} C)) {}\mRightarrow{} ((\mforall{}x:T. (P x)) \mwedge{} C))
Date html generated:
2014_07_17-AM-09_55_54
Last ObjectModification:
2014_06_19-AM-10_57_32
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