Nuprl Lemma : lg-remove-noop
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[x:ℕ]. lg-remove(g;x) ~ g supposing lg-size(g) ≤ x
Proof
Definitions occuring in Statement :
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type,
sqequal: s ~ t
Lemmas :
length_wf_nat,
top_wf,
dep-isect-subtype,
list_wf,
int_seg_wf,
length_wf,
le_wf,
lg-size_wf,
nat_wf,
labeled-graph_wf,
nth_tl_is_nil,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtype_rel_list,
append-nil,
firstn_wf,
firstn_all,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
map_nil_lemma,
product_subtype_list,
spread_cons_lemma,
le_antisymmetry_iff,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
map_cons_lemma,
filter_nil_lemma,
filter_cons_lemma,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_weakening,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
le_int_wf,
assert_of_le_int,
list_subtype_base,
cons_wf
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}]. lg-remove(g;x) \msim{} g supposing lg-size(g) \mleq{} x
Date html generated:
2015_07_22-PM-00_28_25
Last ObjectModification:
2015_01_28-PM-11_33_21
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