Nuprl Lemma : int-decr-map-add-prop
∀[Value:Type]. ∀[m:int-decr-map-type(Value)]. ∀[k1,k2:ℤ]. ∀[v:Value].
(int-decr-map-find(k1;int-decr-map-add(k2;v;m))
= if (k1 =z k2) ∧b (¬bint-decr-map-inDom(k2;m)) then inl v else int-decr-map-find(k1;m) fi
∈ (Value?))
Proof
Definitions occuring in Statement :
int-decr-map-add: int-decr-map-add(k;v;m),
int-decr-map-inDom: int-decr-map-inDom(k;m),
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
band: p ∧b q,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
unit: Unit,
inl: inl x,
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_ind_nil_lemma,
list_ind_cons_lemma,
value-type-has-value,
int-value-type,
subtract_wf,
bool_cases_sqequal,
eq_int_wf,
sqequal-tt-to-assert,
assert_of_eq_int,
sqequal-ff-to-assert,
neg_assert_of_eq_int,
lt_int_wf,
assert_of_lt_int,
it_wf,
less_than_wf,
insert-combine-cons,
int-decr-map-inDom_wf,
l-ordered_wf,
gt_wf,
find-combine-cons,
int-decr-map-inDom-prop2,
l_all_iff,
l_member_wf,
not_wf,
equal-wf-base-T,
int_subtype_base,
cons_member,
unit_wf2,
or_wf,
equal_wf,
l-ordered-cons,
find-combine_wf,
int-decr-map-inDom-cons,
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
eqtt_to_assert,
bnot_wf,
bfalse_wf,
equal-wf-base,
assert_wf,
false_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
assert_elim,
btrue_neq_bfalse,
iff_wf
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)]. \mforall{}[k1,k2:\mBbbZ{}]. \mforall{}[v:Value].
(int-decr-map-find(k1;int-decr-map-add(k2;v;m))
= if (k1 =\msubz{} k2) \mwedge{}\msubb{} (\mneg{}\msubb{}int-decr-map-inDom(k2;m)) then inl v else int-decr-map-find(k1;m) fi )
Date html generated:
2015_07_17-AM-08_23_32
Last ObjectModification:
2015_04_02-PM-05_44_29
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