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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x]
Latex:
\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:
2016_05_17-PM-01_37_42
Last ObjectModification:
2015_12_28-PM-08_11_23
Theory : binary-map
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