Nuprl Lemma : is-dag-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[x:ℕlg-size(g)]. is-dag(lg-remove(g;x)) supposing is-dag(g)
Proof
Definitions occuring in Statement :
is-dag: is-dag(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 :
lg-size-remove,
lg-edge-remove,
less_than_transitivity1,
le_weakening,
lelt_wf,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__lt,
false_wf,
less-iff-le,
le_antisymmetry_iff,
condition-implies-le,
add-associates,
minus-one-mul,
add-commutes,
add-swap,
add_functionality_wrt_le,
le-add-cancel2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
decidable__le,
not-le-2,
sq_stable__le,
minus-add,
zero-add,
add-zero,
le-add-cancel,
lg-size_wf,
lg-remove_wf,
le_wf,
lg-edge_wf,
int_seg_subtype-nat,
int_seg_wf,
member-less_than,
nat_wf,
is-dag_wf,
labeled-graph_wf,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}lg-size(g)]. is-dag(lg-remove(g;x)) supposing is-dag(g)
Date html generated:
2015_07_22-PM-00_29_50
Last ObjectModification:
2015_01_28-PM-11_35_51
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