Nuprl Lemma : State-comb-classrel-single-val
∀[Info,B,A:Type].
∀f:A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
(uiff(v ∈ State-comb(init;f;X)(e);iterated-classrel(es;B;A;f;init;X;e;v))) supposing
(single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
classrel_wf,
es-E_wf,
State-comb-classrel2,
sq_stable__single-valued-iterated-classrel,
State-comb_wf,
iterated-classrel_wf,
single-valued-classrel_wf,
single-valued-bag_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type].
\mforall{}f:A {}\mrightarrow{} B {}\mrightarrow{} B. \mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:B.
(uiff(v \mmember{} State-comb(init;f;X)(e);iterated-classrel(es;B;A;f;init;X;e;v))) supposing
(single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Date html generated:
2015_07_22-PM-00_21_30
Last ObjectModification:
2015_01_28-AM-10_12_13
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