Nuprl Lemma : binary_mapco-ext
∀[T,Key:Type].
binary_mapco(T;Key) ≡ lbl:Atom × if lbl =a "E" then Unit
if lbl =a "T"
then key:Key × value:T × cnt:ℤ × left:binary_mapco(T;Key) × binary_mapco(T;Key)
else Void
fi
Proof
Definitions occuring in Statement :
binary_mapco: binary_mapco(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],
member: t ∈ T,
binary_mapco: binary_mapco(T;Key),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
ext-eq: A ≡ B
Latex:
\mforall{}[T,Key:Type].
binary\_mapco(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\_mapco(T;Key)
\mtimes{} binary\_mapco(T;Key)
else Void
fi
Date html generated:
2016_05_17-PM-01_36_54
Last ObjectModification:
2015_12_28-PM-08_11_21
Theory : binary-map
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