Nuprl Lemma : loop-class-state-functional
∀[Info,B:Type]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(B ─→ B)]. ∀[es:EO+(Info)].
(loop-class-state(X;init) is functional) supposing
((∀l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B ─→ B) and
(∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
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 :
loop-class-state-single-val,
loop-class-state-total,
classrel_wf,
loop-class-state_wf,
es-E_wf,
event-ordering+_subtype,
less_than_wf,
bag-size_wf,
class-ap_wf,
nat_wf,
all_wf,
Id_wf,
single-valued-bag_wf,
single-valued-classrel_wf,
le_wf,
event-ordering+_wf,
eclass_wf,
bag_wf
Latex:
\mforall{}[Info,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[es:EO+(Info)].
(loop-class-state(X;init) is functional) supposing
((\mforall{}l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B {}\mrightarrow{} B) and
(\mforall{}l:Id. (1 \mleq{} \#(init l))))
Date html generated:
2015_07_21-PM-02_33_52
Last ObjectModification:
2015_01_27-PM-09_45_01
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