Nuprl Lemma : fim97_lift_exist
C:
. T:Type. P:T 
. ((R:. (
R 
(
R))) 
(C (
t:T. (P t))) (a:T. (t:T. (C (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,
exists: x:A. B[x],
member: t 
T,
so_lambda: 
x.t[x],
true: True,
or: P Q,
not: A,
uall: [x:A]. B[x],
so_apply: x[s],
false: False
Lemmas :
squash_wf,
exists_wf,
all_wf,
or_wf,
not_wf
\mforall{}C:\mBbbP{}. \mforall{}T:Type. \mforall{}P:T {}\mrightarrow{} \mBbbP{}.
((\mforall{}R:\mBbbP{}. (\mdownarrow{}R \mvee{} (\mneg{}R))) {}\mRightarrow{} (C {}\mRightarrow{} (\mdownarrow{}\mexists{}t:T. (P t))) {}\mRightarrow{} (\mforall{}a:T. (\mdownarrow{}\mexists{}t:T. (C {}\mRightarrow{} (P t)))))
Date html generated:
2013_03_20-AM-10_49_35
Last ObjectModification:
2013_02_26-PM-04_04_06
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