Nuprl Lemma : fpf-cap-single
[A:Type]. [eq:EqDecider(A)]. [x,y:A]. [v,z:Top]. (x : v(y)?z ~ if eqof(eq) x y then v else z fi )
Proof not projected
Definitions occuring in Statement :
fpf-single: x : v,
fpf-cap: f(x)?z,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t,
eqof: eqof(d),
deq: EqDecider(T)
Definitions :
guard: {T},
btrue: tt,
implies: P 
Q,
all: x:A. B[x],
member: t 
T,
bfalse: ff,
bor: p 
q,
reduce: reduce(f;k;as),
pi2: snd(t),
pi1: fst(t),
deq-member: deq-member(eq;x;L),
fpf-ap: f(x),
fpf-dom: x dom(f),
eqof: eqof(d),
ifthenelse: if b then t else f fi ,
fpf-single: x : v,
fpf-cap: f(x)?z,
and: P 
Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
unit: Unit,
uall: [x:A]. B[x],
bool: 
,
deq: EqDecider(T),
it: 
Lemmas :
deq_wf,
top_wf,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
not_wf,
bnot_wf,
assert-deq,
eqtt_to_assert,
assert_wf,
equal_wf,
uiff_transitivity,
bool_wf,
eqof_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x,y:A]. \mforall{}[v,z:Top].
(x : v(y)?z \msim{} if eqof(eq) x y then v else z fi )
Date html generated:
2012_01_23-AM-11_54_59
Last ObjectModification:
2011_12_10-AM-11_58_49
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