Nuprl Lemma : binary_map_ind_wf
∀[T,Key,A:Type]. ∀[R:A ─→ binary_map(T;Key) ─→ ℙ]. ∀[v:binary_map(T;Key)]. ∀[E:{x:A| R[x;bm_E()]} ].
∀[T:key:Key
─→ value:T
─→ cnt:ℤ
─→ left:binary_map(T;Key)
─→ right:binary_map(T;Key)
─→ {x:A| R[x;left]}
─→ {x:A| R[x;right]}
─→ {x:A| R[x;bm_T(key;value;cnt;left;right)]} ].
(binary_map_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2]) ∈ {x:A| R[x;v]} )
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]),
bm_T: bm_T(key;value;cnt;left;right),
bm_E: bm_E(),
binary_map: binary_map(T;Key),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[a;b;c;d;e;f;g],
so_apply: x[s1;s2],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
top_wf,
has-value_wf_base,
lifting-strict-atom_eq,
base_wf,
binary_map_wf,
bm_E_wf,
bm_T_wf,
all_wf,
set_wf,
subtype_rel-equal
\mforall{}[T,Key,A:Type]. \mforall{}[R:A {}\mrightarrow{} binary\_map(T;Key) {}\mrightarrow{} \mBbbP{}]. \mforall{}[v:binary\_map(T;Key)]. \mforall{}[E:\{x:A| R[x;bm\_E()]\} ].
\mforall{}[T:key:Key
{}\mrightarrow{} value:T
{}\mrightarrow{} cnt:\mBbbZ{}
{}\mrightarrow{} left:binary\_map(T;Key)
{}\mrightarrow{} right:binary\_map(T;Key)
{}\mrightarrow{} \{x:A| R[x;left]\}
{}\mrightarrow{} \{x:A| R[x;right]\}
{}\mrightarrow{} \{x:A| R[x;bm\_T(key;value;cnt;left;right)]\} ].
(binary\_map\_ind(v;E;key,value,cnt,left,right,rec1,rec2.T[key;value;cnt;left;right;rec1;rec2])
\mmember{} \{x:A| R[x;v]\} )
Date html generated:
2015_07_17-AM-08_17_55
Last ObjectModification:
2015_01_29-PM-04_40_27
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