Nuprl Lemma : nat-ind-boot-direct
P:
. (((P 0) 
(n:. ((P n) 
(P (n + 1))))) (n:. (P n)))
Proof
Definitions occuring in Statement :
nat: ,
prop: ,
all: x:A. B[x],
implies: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
add: n + m,
natural_number: $n
Definitions :
all: x:A. B[x],
nat: ,
prop: ,
implies: P Q,
and: P Q,
member: t 
T,
le: A 
B,
not: 
A,
false: False,
so_lambda: 
x.t[x],
primrec: primrec(n;b;c),
iff: P 
Q,
rev_implies: P Q,
has-value: (a)
,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
it: 
,
btrue: tt,
bfalse: ff
Lemmas :
nat_wf,
le_wf,
all_wf,
eq_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
subtype_rel_weakening,
ext-eq_weakening,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_base_sq,
int_subtype_base,
subtype_rel_self,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
set-value-type,
int-value-type
\mforall{}P:\mBbbN{} {}\mrightarrow{} \mBbbP{}. (((P 0) \mwedge{} (\mforall{}n:\mBbbN{}. ((P n) {}\mRightarrow{} (P (n + 1))))) {}\mRightarrow{} (\mforall{}n:\mBbbN{}. (P n)))
Date html generated:
2013_03_20-AM-09_46_21
Last ObjectModification:
2012_11_27-AM-10_31_57
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