Nuprl Lemma : State-class-single-val0
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(B)]. ∀[e:E]. ∀[v1,v2:B].
(v1 = v2 ∈ B) supposing
(v1 ∈ State-class(init;f;X)(e) and
v2 ∈ State-class(init;f;X)(e) and
single-valued-bag(init loc(e);B) and
single-valued-classrel(es;X;A))
Proof
Definitions occuring in Statement :
State-class: State-class(init;f;X),
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
State-classrel,
iterated_classrel-single-val,
classrel_wf,
State-class_wf,
single-valued-bag_wf,
es-loc_wf,
event-ordering+_subtype,
single-valued-classrel_wf,
es-E_wf,
Id_wf,
bag_wf,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[e:E].
\mforall{}[v1,v2:B].
(v1 = v2) supposing
(v1 \mmember{} State-class(init;f;X)(e) and
v2 \mmember{} State-class(init;f;X)(e) and
single-valued-bag(init loc(e);B) and
single-valued-classrel(es;X;A))
Date html generated:
2015_07_22-PM-00_20_23
Last ObjectModification:
2015_01_28-AM-10_13_14
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