Nuprl Lemma : binary_map_case-wf2
∀[X,T,Key:Type]. ∀[x:binary-map(T;Key)]. ∀[E:X]. ∀[F:key:Key
⟶ value:T
⟶ cnt:ℤ
⟶ left:binary-map(T;Key)
⟶ right:binary-map(T;Key)
⟶ X].
(binary_map_case(x;E;key,value,cnt,left,right.F[key;value;cnt;left;right]) ∈ X)
Proof
Definitions occuring in Statement :
binary-map: binary-map(T;Key),
binary_map_case: binary_map_case(m;E;key,value,cnt,left,right.F[key; value; cnt; left; right]),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4;s5],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
binary-map: binary-map(T;Key),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bm_E: bm_E(),
binary_map_case: binary_map_case(m;E;key,value,cnt,left,right.F[key; value; cnt; left; right]),
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
bm_T: bm_T(key;value;cnt;left;right),
so_apply: x[s1;s2;s3;s4;s5]
Latex:
\mforall{}[X,T,Key:Type]. \mforall{}[x:binary-map(T;Key)]. \mforall{}[E:X]. \mforall{}[F:key:Key
{}\mrightarrow{} value:T
{}\mrightarrow{} cnt:\mBbbZ{}
{}\mrightarrow{} left:binary-map(T;Key)
{}\mrightarrow{} right:binary-map(T;Key)
{}\mrightarrow{} X].
(binary\_map\_case(x;E;key,value,cnt,left,right.F[key;value;cnt;left;right]) \mmember{} X)
Date html generated:
2016_05_17-PM-01_38_58
Last ObjectModification:
2015_12_28-PM-08_10_01
Theory : binary-map
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