Nuprl Lemma : boolean_as_01
b:
. (if b then 0 else 1 fi = 0 
b)
Proof
Definitions occuring in Statement :
assert: b,
ifthenelse: if b then t else f fi ,
bool: ,
nat: 
,
all: x:A. B[x],
iff: P Q,
natural_number: $n,
equal: s = t
Definitions :
all: x:A. B[x],
iff: P Q,
nat: ,
ifthenelse: if b then t else f fi ,
and: P 
Q,
implies: P Q,
rev_implies: P Q,
member: t 
T,
btrue: tt,
le: A 
B,
not: 
A,
false: False,
bfalse: ff,
exists: 
x:A. B[x],
squash: 
T,
true: True,
so_lambda: 
x.t[x],
bool: ,
assert: b,
prop: 
,
uall: [x:A]. B[x],
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
bnot: 
b,
or: P 
Q,
sq_type: SQType(T),
guard: {T},
so_apply: x[s],
it: 
Lemmas :
equal_wf,
nat_wf,
bool_wf,
eqtt_to_assert,
le_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
assert_elim,
and_wf,
ifthenelse_wf,
assert_wf,
bool_cases,
assert_of_bnot,
subtype_rel_set_simple
\mforall{}b:\mBbbB{}. (if b then 0 else 1 fi = 0 \mLeftarrow{}{}\mRightarrow{} \muparrow{}b)
Date html generated:
2013_03_20-AM-10_35_22
Last ObjectModification:
2013_03_11-PM-04_58_31
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