Nuprl Lemma : completeInductionShortExt
P:
. ((n:. ((m:n. (P m)) 
(P n))) (n:. (P n)))
Proof
Definitions occuring in Statement :
int_seg: {i..j
},
nat: ,
prop: ,
all: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
natural_number: $n
Definitions :
all: x:A. B[x],
nat: ,
prop: ,
implies: P Q,
member: t 
T,
so_lambda: 
x.t[x],
and: P 
Q,
int_seg: {i..j},
lelt: i 
j < k,
not: 
A,
iff: P 
Q,
rev_implies: P Q,
le: A B,
squash: 
T,
true: True,
false: False,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P 
Q,
it: 
,
btrue: tt,
guard: {T},
bfalse: ff
Lemmas :
nat_wf,
all_wf,
int_seg_wf,
le_wf,
nat-ind-boot,
eq_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
subtype_rel_weakening,
ext-eq_weakening,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
lelt_wf,
and_wf,
decidable__equal_nat,
nat-ind-boot-direct,
decidable__equal_int
\mforall{}P:\mBbbN{} {}\mrightarrow{} \mBbbP{}. ((\mforall{}n:\mBbbN{}. ((\mforall{}m:\mBbbN{}n. (P m)) {}\mRightarrow{} (P n))) {}\mRightarrow{} (\mforall{}n:\mBbbN{}. (P n)))
Date html generated:
2013_03_20-AM-09_46_46
Last ObjectModification:
2012_11_27-AM-10_31_58
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