Nuprl Lemma : State-comb-functional
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)].
(State-comb(init;f;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(∀l:Id. single-valued-bag(init l;B)) and
(∀l:Id. (1 ≤ #(init l))))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;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 :
State-comb-single-val,
State-comb-total,
classrel_wf,
State-comb_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,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
(State-comb(init;f;X) is functional) supposing
(single-valued-classrel(es;X;A) and
(\mforall{}l:Id. single-valued-bag(init l;B)) and
(\mforall{}l:Id. (1 \mleq{} \#(init l))))
Date html generated:
2015_07_22-PM-00_21_42
Last ObjectModification:
2015_01_28-AM-10_12_16
Home
Index