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
Lemmas :
binary_mapco-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
value-type-has-value,
int-value-type,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
binary_mapco_size_wf,
binary_map_wf,
binary_mapco_wf,
add-nat,
false_wf,
binary_map_size_wf,
nat_properties
\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:
2015_07_17-AM-08_17_35
Last ObjectModification:
2015_01_29-PM-04_40_10
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