Nuprl Lemma : state-class1-fun-eq
∀[Info,B,A:Type]. ∀[init:Id ─→ B]. ∀[tr:Id ─→ A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
state-class1(init;tr;X)(e)
= if e ∈b X then if first(e) then tr loc(e) X@e (init loc(e)) else tr loc(e) X@e state-class1(init;tr;X)(pred(e)) fi
if first(e) then init loc(e)
else state-class1(init;tr;X)(pred(e))
fi
∈ B
supposing single-valued-classrel(es;X;A)
Proof
Definitions occuring in Statement :
state-class1: state-class1(init;tr;X),
classfun-res: X@e,
classfun: X(e),
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
loop-class-state-fun-eq,
single-bag_wf,
eclass1_wf,
bag_size_single_lemma,
assert_of_le_int,
eclass1-single-val,
single-valued-bag-single,
member-eclass_wf,
bool_wf,
eqtt_to_assert,
es-first_wf2,
es-loc_wf,
classfun-res_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
classfun_wf,
state-class1_wf,
loop-class-state-functional,
false_wf,
es-pred_wf,
iff_weakening_equal,
sv_bag_only_single_lemma,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
member-eclass-eclass1,
classfun-res-eclass1
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[tr:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
state-class1(init;tr;X)(e)
= if e \mmember{}\msubb{} X
then if first(e)
then tr loc(e) X@e (init loc(e))
else tr loc(e) X@e state-class1(init;tr;X)(pred(e))
fi
if first(e) then init loc(e)
else state-class1(init;tr;X)(pred(e))
fi
supposing single-valued-classrel(es;X;A)
Date html generated:
2015_07_23-AM-11_30_09
Last ObjectModification:
2015_02_04-PM-04_43_48
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