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
Lemmas :
es-interface-local-state-prior,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
and_wf,
equal_wf,
eclass-val_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
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:
2015_07_21-PM-03_43_13
Last ObjectModification:
2015_01_27-PM-06_26_55
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