Nuprl Lemma : lg-edge-remove
[T:Type]
g:LabeledGraph(T). i:
lg-size(g). a,b:lg-size(g) - 1.
(lg-edge(lg-remove(g;i);a;b) 
lg-edge(g;if a <z i then a else a + 1 fi ;if b <z i then b else b + 1 fi ))
Proof not projected
Definitions occuring in Statement :
lg-edge: lg-edge(g;a;b),
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
int_seg: {i..j
},
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type
Definitions :
member: t 
T,
top: Top,
lg-in-edges: lg-in-edges(g;x),
lg-remove: lg-remove(g;n),
lg-edge: lg-edge(g;a;b),
all: x:A. B[x],
uall: [x:A]. B[x],
lg-size: lg-size(g),
nat: ,
iff: P Q,
rev_implies: P Q,
false: False,
implies: P Q,
not: 
A,
le: A 
B,
and: P 
Q,
lelt: i j < k,
int_seg: {i..j},
bfalse: ff,
prop: 
,
btrue: tt,
ifthenelse: if b then t else f fi ,
int_iseg: {i...j},
true: True,
squash: 
T,
spreadn: spread3,
pi2: snd(t),
pi1: fst(t),
so_lambda: 
x.t[x],
subtype: S 
T,
cand: A c B,
guard: {T},
exists: 
x:A. B[x],
labeled-graph: LabeledGraph(T),
uimplies: b supposing a,
unit: Unit,
bool: 
,
so_apply: x[s],
sq_type: SQType(T),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
it: 
Lemmas :
labeled-graph_wf,
nat_wf,
lg-size_wf,
int_seg_wf,
nth_tl_wf,
firstn_wf,
top_wf,
append_wf,
select-map,
length-map-sq,
lg-remove_wf,
le_wf,
lg-size-remove,
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,
select_firstn,
select_append_front,
select_wf,
length_wf,
length_firstn,
length_nth_tl,
add_functionality_wrt_eq,
select_nth_tl,
select_append_back,
length_wf_nat,
non_neg_length,
true_wf,
squash_wf,
ifthenelse_wf,
equal_wf,
and_wf,
exists_wf,
eq_int_wf,
filter_wf,
map_wf,
l_member_wf,
iff_functionality_wrt_iff,
member_map,
exists_functionality_wrt_iff,
and_functionality_wrt_iff,
member_filter,
int_subtype_base,
subtype_base_sq,
bnot_of_le_int,
less_than_wf,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
assert_of_eq_int,
implies_functionality_wrt_iff,
pi2_wf,
pi1_wf_top,
iff_wf
\mforall{}[T:Type]
\mforall{}g:LabeledGraph(T). \mforall{}i:\mBbbN{}lg-size(g). \mforall{}a,b:\mBbbN{}lg-size(g) - 1.
(lg-edge(lg-remove(g;i);a;b)
\mLeftarrow{}{}\mRightarrow{} lg-edge(g;if a <z i then a else a + 1 fi ;if b <z i then b else b + 1 fi ))
Date html generated:
2012_01_23-PM-12_38_06
Last ObjectModification:
2012_01_05-PM-02_49_13
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