Nuprl Lemma : es-interface-local-state_wf
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,T:Type]. ∀[X:EClass(A)]. ∀[base:T]. ∀[f:T ⟶ A ⟶ T]. ∀[e:E].
(local-state(f;base;X;e) ∈ T)
Proof
Definitions occuring in Statement :
es-interface-local-state: local-state(f;base;X;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-interface-local-state: local-state(f;base;X;e),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,T:Type]. \mforall{}[X:EClass(A)]. \mforall{}[base:T]. \mforall{}[f:T {}\mrightarrow{} A {}\mrightarrow{} T]. \mforall{}[e:E].
(local-state(f;base;X;e) \mmember{} T)
Date html generated:
2016_05_17-AM-07_09_58
Last ObjectModification:
2015_12_29-AM-00_11_51
Theory : event-ordering
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