Nuprl Lemma : int-decr-map-find-not-in
∀[Value:Type]. ∀[k:ℤ]. ∀[m:int-decr-map-type(Value)].
int-decr-map-find(k;m) = (inr ⋅ ) ∈ (Value?) supposing (∀p∈m.¬(k = (fst(p)) ∈ ℤ))
Proof
Definitions occuring in Statement :
int-decr-map-find: int-decr-map-find(k;m),
int-decr-map-type: int-decr-map-type(Value),
l_all: (∀x∈L.P[x]),
it: ⋅,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
not: ¬A,
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_all_wf2,
l_member_wf,
not_wf,
equal-wf-base-T,
l-ordered_wf,
gt_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
it_wf,
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,
int_subtype_base,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
l_all_cons,
l-ordered-cons,
find-combine-cons,
value-type-has-value,
int-value-type,
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,
cons_wf,
int-decr-map-type_wf
\mforall{}[Value:Type]. \mforall{}[k:\mBbbZ{}]. \mforall{}[m:int-decr-map-type(Value)].
int-decr-map-find(k;m) = (inr \mcdot{} ) supposing (\mforall{}p\mmember{}m.\mneg{}(k = (fst(p))))
Date html generated:
2015_07_17-AM-08_22_56
Last ObjectModification:
2015_04_02-PM-05_44_02
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