Nuprl Lemma : int-decr-map-isEmpty-prop
∀[Value:Type]. ∀[m:int-decr-map-type(Value)]. (↑int-decr-map-isEmpty(m) ⇐⇒ ∀k:ℤ. (¬↑int-decr-map-inDom(k;m)))
Proof
Definitions occuring in Statement :
int-decr-map-isEmpty: int-decr-map-isEmpty(m),
int-decr-map-inDom: int-decr-map-inDom(k;m),
int-decr-map-type: int-decr-map-type(Value),
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
int: ℤ,
universe: Type
Definitions :
not: ¬A,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
int-decr-map-inDom: int-decr-map-inDom(k;m),
isl: isl(x),
int-decr-map-find: int-decr-map-find(k;m),
find-combine: find-combine(cmp;l),
int-decr-map-empty: int-decr-map-empty(),
nil: [],
it: ⋅,
bfalse: ff,
false: False
Lemmas :
int-decr-map-isEmpty-assert,
not_wf,
assert_wf,
int-decr-map-inDom_wf,
int-decr-map-isEmpty_wf,
decidable__assert,
assert_of_null,
equal-wf-T-base,
list_wf,
member_exists,
int-decr-map-inDom-prop,
isl_wf,
null_wf3,
subtype_rel_list,
top_wf,
l_member_wf,
squash_wf,
l_all_wf2,
equal-wf-base-T,
int_subtype_base,
int-decr-map-find_wf,
int-decr-map-find-prop2,
l_all_iff,
all_wf,
assert_witness,
int-decr-map-type_wf
\mforall{}[Value:Type]. \mforall{}[m:int-decr-map-type(Value)].
(\muparrow{}int-decr-map-isEmpty(m) \mLeftarrow{}{}\mRightarrow{} \mforall{}k:\mBbbZ{}. (\mneg{}\muparrow{}int-decr-map-inDom(k;m)))
Date html generated:
2015_07_17-AM-08_23_16
Last ObjectModification:
2015_04_02-PM-05_44_20
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