Nuprl Lemma : conditional_wf2
[T,V:Type]. [A,B:T 
]. [dcd_A:t:T Dec(A[t])]. [f:{t:T| A[t]} V]. [g:{t:T| B[t]} V].
([
t.A[t]? f : g] 
{t:T| A[t] 
B[t]} V)
Proof not projected
Definitions occuring in Statement :
conditional: [P? f : g],
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
or: P Q,
member: t T,
set: {x:A| B[x]} ,
lambda: x.A[x],
function: x:A B[x],
universe: Type
Definitions :
suptype: suptype(S; T),
subtype: S 
T,
all: x:A. B[x],
or: P Q,
uall: [x:A]. B[x],
member: t T,
so_apply: x[s],
prop: ,
implies: P 
Q,
so_lambda: 
x.t[x],
cand: A c
B,
and: P Q,
uimplies: b supposing a,
false: False,
not: 
A
Lemmas :
decidable_wf,
or_wf,
conditional_wf,
subtype_rel_self,
subtype_rel_sets,
subtype_rel_nested_set2,
subtype_rel_dep_function,
and_wf,
not_wf
\mforall{}[T,V:Type]. \mforall{}[A,B:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[dcd$_{A}$:t:T {}\mrightarrow{} Dec(A[t])]. \mforall{}[f:\{t:T| A[t]\} {}\mrightarrow{} V\000C]. \mforall{}[g:\{t:T| B[t]\} {}\mrightarrow{} V].
([\mlambda{}t.A[t]? f : g] \mmember{} \{t:T| A[t] \mvee{} B[t]\} {}\mrightarrow{} V)
Date html generated:
2012_01_23-PM-12_14_31
Last ObjectModification:
2011_12_13-PM-12_47_29
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