Nuprl Lemma : bm_lookup_wf
∀[T,Key:Type]. ∀[compare:bm_compare(Key)]. ∀[x:Key]. ∀[m:binary-map(T;Key)].
bm_lookup(compare;m;x) ∈ T supposing ↑bm_inDomain(compare;m;x)
Proof
Definitions occuring in Statement :
bm_lookup: bm_lookup(compare;m;x),
bm_inDomain: bm_inDomain(compare;m;x),
bm_compare: bm_compare(K),
binary-map: binary-map(T;Key),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
assert_wf,
bm_inDomain_wf,
bm_cnt_prop_wf,
le_wf,
binary_map_size_wf,
int_seg_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
binary_map-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
bm_cnt_prop_E,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
not-le-2,
subtract-is-less,
lelt_wf,
bm_cnt_prop_T,
bm_T_wf,
equal-wf-base-T,
int_subtype_base,
bm_numItems_wf,
bm_T-wf2,
member_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
sq_stable__le,
add-mul-special,
zero-mul,
nat_wf,
binary_map_wf,
binary-map_wf,
bm_compare_wf,
valueall-type-has-valueall,
int-valueall-type,
lt_int_wf,
assert_of_lt_int,
iff_imp_equal_bool,
btrue_wf,
iff_wf,
evalall-reduce
\mforall{}[T,Key:Type]. \mforall{}[compare:bm\_compare(Key)]. \mforall{}[x:Key]. \mforall{}[m:binary-map(T;Key)].
bm\_lookup(compare;m;x) \mmember{} T supposing \muparrow{}bm\_inDomain(compare;m;x)
Date html generated:
2015_07_17-AM-08_19_52
Last ObjectModification:
2015_01_27-PM-00_37_45
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