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 unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
false: False
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
int-decr-map-inDom: int-decr-map-inDom(k;m)
, 
isl: isl(x)
, 
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w])
, 
so_apply: x[s1;s2;s3;s4]
, 
so_lambda: λ2x.t[x]
, 
top: Top
, 
so_apply: x[s]
, 
strict4: strict4(F)
, 
has-value: (a)↓
, 
prop: ℙ
, 
guard: {T}
, 
or: P ∨ Q
, 
squash: ↓T
, 
int-decr-map-find: int-decr-map-find(k;m)
, 
find-combine: find-combine(cmp;l)
, 
list_ind: list_ind, 
int-decr-map-empty: int-decr-map-empty()
, 
nil: []
, 
it: ⋅
, 
bfalse: ff
, 
rev_implies: P 
⇐ Q
, 
decidable: Dec(P)
, 
int-decr-map-isEmpty: int-decr-map-isEmpty(m)
, 
int-decr-map-type: int-decr-map-type(Value)
, 
exists: ∃x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
pi1: fst(t)
Latex:
\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:
2016_05_17-PM-01_48_44
Last ObjectModification:
2016_01_18-PM-06_43_31
Theory : datatype-signatures
Home
Index