Nuprl Lemma : lg-acyclic-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[i:ℕlg-size(g)]. lg-acyclic(lg-remove(g;i)) supposing lg-acyclic(g)
Proof
Definitions occuring in Statement :
lg-acyclic: lg-acyclic(g),
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Lemmas :
subtype_base_sq,
int_subtype_base,
lg-size-remove,
subtract_wf,
iff_weakening_equal,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__lt,
lg-size_wf,
false_wf,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
lelt_wf,
nat_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
less_than_wf,
decidable__le,
not-le-2,
sq_stable__le,
zero-add,
add-zero,
le-add-cancel,
lg-connected_wf,
int_seg_wf,
lg-remove_wf,
int_seg_subtype-nat,
lg-acyclic_wf,
labeled-graph_wf,
lg-connected-remove
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)].
\mforall{}[i:\mBbbN{}lg-size(g)]. lg-acyclic(lg-remove(g;i)) supposing lg-acyclic(g)
Date html generated:
2015_07_22-PM-00_29_13
Last ObjectModification:
2015_02_04-PM-04_50_45
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