Nuprl Lemma : lg-size-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[x:ℕlg-size(g)]. (lg-size(lg-remove(g;x)) = (lg-size(g) - 1) ∈ ℤ)
Proof
Definitions occuring in Statement :
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
length-map-sq,
append_wf,
top_wf,
firstn_wf,
dep-isect-subtype,
list_wf,
int_seg_wf,
length_wf,
nth_tl_wf,
length-append,
lg-size_wf,
nat_wf,
labeled-graph_wf,
length_nth_tl,
subtract_wf,
add_functionality_wrt_eq,
iff_weakening_equal,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
sq_stable__le,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
less-iff-le,
le-add-cancel2,
le_wf,
length_firstn,
le_weakening2,
member_wf,
squash_wf,
true_wf,
add-mul-special,
zero-mul
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}lg-size(g)]. (lg-size(lg-remove(g;x)) = (lg-size(g) - 1))
Date html generated:
2015_07_22-PM-00_28_28
Last ObjectModification:
2015_02_04-PM-04_03_26
Home
Index