Nuprl Lemma : es-interface-local-state-cases
∀[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)
= if e ∈b X then f if e ∈b prior(X) then local-state(f;base;X;prior(X)(e)) else base fi X(e)
if e ∈b prior(X) then local-state(f;base;X;prior(X)(e))
else base
fi
∈ T)
Proof
Definitions occuring in Statement :
es-interface-local-state: local-state(f;base;X;e),
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
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],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff
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)
= if e \mmember{}\msubb{} X then f if e \mmember{}\msubb{} prior(X) then local-state(f;base;X;prior(X)(e)) else base fi X(e)
if e \mmember{}\msubb{} prior(X) then local-state(f;base;X;prior(X)(e))
else base
fi )
Date html generated:
2016_05_17-AM-07_10_36
Last ObjectModification:
2015_12_29-AM-00_11_00
Theory : event-ordering
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