Nuprl Lemma : hw5_3_3_2
T:Type. A,B:T 
T 
.
((P:. (P 
(
P)))
((
y:T. x:T. (A x y)) (z:T. x:T. (B x z)))
(y:T. z:T. ((x:T. (A x y)) (x:T. (B x z)))))
Proof
Definitions occuring in Statement :
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
or: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
so_lambda: 
x.t[x],
member: t 
T,
or: P Q,
implies: P Q,
prop: ,
all: x:A. B[x],
exists: x:A. B[x],
so_apply: x[s],
uall: [x:A]. B[x],
not: A,
false: False,
guard: {T}
Lemmas :
not_wf,
or_wf,
all_wf,
exists_wf
\mforall{}T:Type. \mforall{}A,B:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}.
((\mforall{}P:\mBbbP{}. (P \mvee{} (\mneg{}P)))
{}\mRightarrow{} ((\mexists{}y:T. \mforall{}x:T. (A x y)) {}\mRightarrow{} (\mexists{}z:T. \mforall{}x:T. (B x z)))
{}\mRightarrow{} (\mforall{}y:T. \mexists{}z:T. ((\mforall{}x:T. (A x y)) {}\mRightarrow{} (\mforall{}x:T. (B x z)))))
Date html generated:
2013_03_20-AM-09_55_10
Last ObjectModification:
2012_11_27-AM-10_33_34
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