Nuprl Lemma : lg-all-remove
[T:Type]. [P:T 
]. g:LabeledGraph(T). x:
lg-size(g). (x
g.P[x] 
xlg-remove(g;x).P[x] 
P[lg-label(g;x)])
Proof not projected
Definitions occuring in Statement :
lg-all: xG.P[x],
lg-label: lg-label(g;x),
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j
},
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
and: P Q,
function: x:A B[x],
natural_number: $n,
universe: Type
Definitions :
so_lambda: 
x.t[x],
nat: ,
member: t T,
rev_implies: P Q,
implies: P Q,
and: P Q,
so_apply: x[s],
lg-all: xG.P[x],
iff: P Q,
all: x:A. B[x],
prop: ,
uall: [x:A]. B[x],
true: True,
squash: 
T,
lg-label2: lg-label2(g;x),
false: False,
not: 
A,
bfalse: ff,
btrue: tt,
le: A 
B,
ifthenelse: if b then t else f fi ,
lelt: i j < k,
int_seg: {i..j},
uimplies: b supposing a,
unit: Unit,
bool: 
,
or: P 
Q,
decidable: Dec(P),
guard: {T},
sq_type: SQType(T),
it: 
Lemmas :
labeled-graph_wf,
and_wf,
lg-label2_wf,
all_wf,
nat_wf,
le_wf,
lg-remove_wf,
lg-size_wf,
int_seg_wf,
lg-size-remove,
true_wf,
squash_wf,
lelt_wf,
int_seg_properties,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
le_int_wf,
assert_of_lt_int,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
iff_weakening_uiff,
bool_wf,
lt_int_wf,
lg-label-remove,
decidable__lt,
bool_subtype_base,
subtype_base_sq,
bool_cases,
int_subtype_base
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}].
\mforall{}g:LabeledGraph(T). \mforall{}x:\mBbbN{}lg-size(g). (\mforall{}x\mmember{}g.P[x] \mLeftarrow{}{}\mRightarrow{} \mforall{}x\mmember{}lg-remove(g;x).P[x] \mwedge{} P[lg-label(g;x)])
Date html generated:
2012_01_23-PM-12_41_16
Last ObjectModification:
2012_01_06-AM-10_23_48
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