Nuprl Lemma : binary_map-definition
∀[T,Key,A:Type]. ∀[R:A ─→ binary_map(T;Key) ─→ ℙ].
({x:A| R[x;bm_E()]}
⇒ (∀key:Key. ∀value:T. ∀cnt:ℤ. ∀left,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)]} ))
⇒ {∀v:binary_map(T;Key). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
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,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
binary_map-induction,
set_wf,
binary_map_wf,
all_wf,
bm_T_wf,
bm_E_wf
\mforall{}[T,Key,A:Type]. \mforall{}[R:A {}\mrightarrow{} binary\_map(T;Key) {}\mrightarrow{} \mBbbP{}].
(\{x:A| R[x;bm\_E()]\}
{}\mRightarrow{} (\mforall{}key:Key. \mforall{}value:T. \mforall{}cnt:\mBbbZ{}. \mforall{}left,right:binary\_map(T;Key).
(\{x:A| R[x;left]\} {}\mRightarrow{} \{x:A| R[x;right]\} {}\mRightarrow{} \{x:A| R[x;bm\_T(key;value;cnt;left;right)]\} ))
{}\mRightarrow{} \{\mforall{}v:binary\_map(T;Key). \{x:A| R[x;v]\} \})
Date html generated:
2015_07_17-AM-08_17_54
Last ObjectModification:
2015_01_27-PM-00_40_27
Home
Index