Nuprl Lemma : lg-label-map
∀[f:Top]. ∀[g:LabeledGraph(Top)]. ∀[x:ℕlg-size(g)]. (lg-label(lg-map(f;g);x) ~ f lg-label(g;x))
Proof
Definitions occuring in Statement :
lg-map: lg-map(f;g),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions :
select: L[n],
nil: [],
it: ⋅
Lemmas :
list_wf,
top_wf,
int_seg_wf,
nat_wf,
less_than_wf,
length_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
length_of_nil_lemma,
map_nil_lemma,
stuck-spread,
base_wf,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
length_of_cons_lemma,
map_cons_lemma,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
minus-zero,
decidable__lt,
lg-size_wf,
le-add-cancel2,
lelt_wf,
select-cons
Latex:
\mforall{}[f:Top]. \mforall{}[g:LabeledGraph(Top)]. \mforall{}[x:\mBbbN{}lg-size(g)]. (lg-label(lg-map(f;g);x) \msim{} f lg-label(g;x))
Date html generated:
2015_07_23-AM-11_04_25
Last ObjectModification:
2015_01_28-PM-11_35_37
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