Nuprl Lemma : int-decr-map-remove-prop
∀[Value:Type]. ∀[m:int-decr-map-type(Value)]. ∀[k1,k2:ℤ].
(int-decr-map-find(k1;int-decr-map-remove(k2;m))
= if (k1 =z k2) then inr ⋅ else int-decr-map-find(k1;m) fi
∈ (Value?))
Proof
Definitions occuring in Statement :
int-decr-map-remove: int-decr-map-remove(k;m),
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
it: ⋅,
uall: ∀[x:A]. B[x],
unit: Unit,
inr: inr x ,
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
l-ordered_wf,
gt_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
it_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nil_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,
nat_wf,
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,
set_subtype_base,
int_subtype_base,
cons_wf,
int-decr-map-type_wf,
remove-combine-cons,
sqequal-tt-to-assert,
l-ordered-cons,
int-decr-map-find-not-in,
l_all_iff,
l_member_wf,
not_wf,
equal-wf-base-T,
sqequal-ff-to-assert,
find-combine-cons,
value-type-has-value,
int-value-type,
lt_int_wf,
assert_of_lt_int,
int-decr-map-find_wf,
cons_wf_listp,
subtype_rel_sets,
list_wf,
assert_wf,
length_wf,
subtype_rel_sum,
null_wf3,
subtype_rel_list,
top_wf,
squash_wf,
l_all_wf2,
unit_wf2,
null_cons_lemma,
subtype_rel-equal
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)]. \mforall{}[k1,k2:\mBbbZ{}].
(int-decr-map-find(k1;int-decr-map-remove(k2;m))
= if (k1 =\msubz{} k2) then inr \mcdot{} else int-decr-map-find(k1;m) fi )
Date html generated:
2015_07_17-AM-08_23_38
Last ObjectModification:
2015_04_02-PM-05_44_33
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