Nuprl Lemma : binary_map-ext
∀[T,Key:Type].
binary_map(T;Key) ≡ lbl:Atom × if lbl =a "E" then Unit
if lbl =a "T"
then key:Key × value:T × cnt:ℤ × left:binary_map(T;Key) × binary_map(T;Key)
else Void
fi
Proof
Definitions occuring in Statement :
binary_map: binary_map(T;Key),
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
unit: Unit,
product: x:A × B[x],
int: ℤ,
token: "$token",
atom: Atom,
void: Void,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
binary_map: binary_map(T;Key),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
binary_mapco_size: binary_mapco_size(p),
has-value: (a)↓,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
binary_map_size: binary_map_size(p),
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A
Latex:
\mforall{}[T,Key:Type].
binary\_map(T;Key) \mequiv{} lbl:Atom \mtimes{} if lbl =a "E" then Unit
if lbl =a "T"
then key:Key
\mtimes{} value:T
\mtimes{} cnt:\mBbbZ{}
\mtimes{} left:binary\_map(T;Key)
\mtimes{} binary\_map(T;Key)
else Void
fi
Date html generated:
2016_05_17-PM-01_37_06
Last ObjectModification:
2016_01_17-AM-11_20_33
Theory : binary-map
Home
Index