Nuprl Lemma : binary_map_ind-wf2
∀[X,T,Key:Type]. ∀[x:binary-map(T;Key)]. ∀[E:X]. ∀[F:key:Key
─→ value:T
─→ cnt:ℤ
─→ left:binary-map(T;Key)
─→ right:binary-map(T;Key)
─→ X
─→ X
─→ X].
(binary_map_ind(x;E;key,value,cnt,left,right,recL,recR.F[key;value;cnt;left;right;recL;recR]) ∈ X)
Proof
Definitions occuring in Statement :
binary-map: binary-map(T;Key),
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
uall: ∀[x:A]. B[x],
so_apply: x[a;b;c;d;e;f;g],
member: t ∈ T,
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
assert_wf,
bm_cnt_prop_wf,
le_wf,
binary_map_size_wf,
binary_map_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_reduce_lemma,
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,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
sq_stable__le,
add-mul-special,
zero-mul,
nat_wf,
binary-map_wf
\mforall{}[X,T,Key:Type]. \mforall{}[x:binary-map(T;Key)]. \mforall{}[E:X]. \mforall{}[F:key:Key
{}\mrightarrow{} value:T
{}\mrightarrow{} cnt:\mBbbZ{}
{}\mrightarrow{} left:binary-map(T;Key)
{}\mrightarrow{} right:binary-map(T;Key)
{}\mrightarrow{} X
{}\mrightarrow{} X
{}\mrightarrow{} X].
(binary\_map\_ind(x;E;key,value,cnt,left,right,recL,recR.F[key;value;cnt;left;right;recL;recR]) \mmember{} X)
Date html generated:
2015_07_17-AM-08_18_40
Last ObjectModification:
2015_01_27-PM-00_40_28
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