Nuprl Lemma : lg-label-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[k:ℕlg-size(g)]. ∀[x:ℕlg-size(g) - 1].
(lg-label(lg-remove(g;k);x) ~ if x <z k then lg-label(g;x) else lg-label(g;x + 1) fi )
Proof
Definitions occuring in Statement :
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-},
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Lemmas :
lg-size_wf,
int_seg_wf,
subtract_wf,
nat_wf,
labeled-graph_wf,
select-map,
append_wf,
list_wf,
firstn_wf,
nth_tl_wf,
subtype_rel_list,
top_wf,
length-append,
lelt_wf,
length_wf,
select-append,
int_seg_subtype-nat,
false_wf,
length-map-sq,
lg-size-remove,
less_than_wf,
squash_wf,
true_wf,
iff_weakening_equal,
length_firstn,
subtype_rel_sets,
le_wf,
le_weakening2,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
select-firstn,
select_wf,
decidable__lt,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
int_seg_properties,
select-nth_tl,
decidable__le,
not-le-2,
zero-add,
sq_stable__le,
add-zero,
le-add-cancel,
zero-le-nat,
int_subtype_base,
add-mul-special,
zero-mul
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[k:\mBbbN{}lg-size(g)]. \mforall{}[x:\mBbbN{}lg-size(g) - 1].
(lg-label(lg-remove(g;k);x) \msim{} if x <z k then lg-label(g;x) else lg-label(g;x + 1) fi )
Date html generated:
2015_07_23-AM-11_04_32
Last ObjectModification:
2015_02_04-PM-04_50_34
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