Nuprl Lemma : Memory-class-functional
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(Memory-class(f;init;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(∀l:Id. single-valued-bag(init l;S)) and
(∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag-size: #(bs),
bag: bag(T)
Lemmas :
Memory-class-single-val,
Memory-class-total,
classrel_wf,
Memory-class_wf,
es-E_wf,
event-ordering+_subtype,
less_than_wf,
bag-size_wf,
class-ap_wf,
nat_wf,
single-valued-classrel_wf,
all_wf,
Id_wf,
single-valued-bag_wf,
le_wf,
event-ordering+_wf,
eclass_wf,
bag_wf
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
(Memory-class(f;init;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(\mforall{}l:Id. single-valued-bag(init l;S)) and
(\mforall{}l:Id. (1 \mleq{} \#(init l))))
Date html generated:
2015_07_22-PM-00_13_02
Last ObjectModification:
2015_01_28-AM-10_46_52
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