Nuprl Lemma : lex-pair_wf
[S,T:Type]. [ord1:S 
S 
]. [ord2:T T ]. (lex-pair(S;ord1;ord2) 
S 
T S T )
Proof not projected
Definitions occuring in Statement :
lex-pair: lex-pair(S;ord1;ord2),
uall: [x:A]. B[x],
prop: ,
member: t T,
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
void: Void,
so_lambda: 
x.t[x],
pi2: snd(t),
limited-type: LimitedType,
and: P 
Q,
subtype: S 
T,
top: Top,
all: x:A. B[x],
pi1: fst(t),
apply: f a,
union: left + right,
or: P 
Q,
lambda: x.A[x],
axiom: Ax,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
function: x:A B[x],
product: x:A B[x],
prop: ,
universe: Type,
lex-pair: lex-pair(S;ord1;ord2)
Lemmas :
pi1_wf_top,
pi2_wf,
top_wf,
member_wf
\mforall{}[S,T:Type]. \mforall{}[ord1:S {}\mrightarrow{} S {}\mrightarrow{} \mBbbP{}]. \mforall{}[ord2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
(lex-pair(S;ord1;ord2) \mmember{} S \mtimes{} T {}\mrightarrow{} S \mtimes{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2011_10_20-PM-04_50_50
Last ObjectModification:
2011_05_19-AM-11_32_12
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