Nuprl Lemma : binary_map_ind_wf_simple
∀[T,Key,A:Type]. ∀[v:binary_map(T;Key)]. ∀[E:A]. ∀[T:key:Key
⟶ value:T
⟶ cnt:ℤ
⟶ left:binary_map(T;Key)
⟶ right:binary_map(T;Key)
⟶ A
⟶ A
⟶ A].
(binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]) ∈ A)
Proof
Definitions occuring in Statement :
binary_map_ind: binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]),
binary_map: binary_map(T;Key),
uall: ∀[x:A]. B[x],
so_apply: x[a;b;c;d;e;f;g],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T}
Latex:
\mforall{}[T,Key,A:Type]. \mforall{}[v:binary\_map(T;Key)]. \mforall{}[E:A]. \mforall{}[T:key:Key
{}\mrightarrow{} value:T
{}\mrightarrow{} cnt:\mBbbZ{}
{}\mrightarrow{} left:binary\_map(T;Key)
{}\mrightarrow{} right:binary\_map(T;Key)
{}\mrightarrow{} A
{}\mrightarrow{} A
{}\mrightarrow{} A].
(binary\_map\_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]) \mmember{} A)
Date html generated:
2016_05_17-PM-01_37_48
Last ObjectModification:
2015_12_28-PM-08_11_15
Theory : binary-map
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