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
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