Nuprl Lemma : State2-functional
∀[Info,A1,A2,S:Type]. ∀[init:Id ─→ S]. ∀[tr1:Id ─→ A1 ─→ S ─→ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ─→ A2 ─→ S ─→ S].
∀[X2:EClass(A2)].
∀es:EO+(Info)
(single-valued-classrel(es;X1;A1)
⇒ single-valued-classrel(es;X2;A2)
⇒ disjoint-classrel(es;A1;X1;A2;X2)
⇒ State2(init;tr1;X1;tr2;X2) is functional)
Proof
Definitions occuring in Statement :
State2: State2(init;tr1;X1;tr2;X2),
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
State-loc-comb-functional,
disjoint-union-tr_wf,
single-bag_wf,
disjoint-union-comb_wf,
bag_size_single_lemma,
false_wf,
single-valued-bag-single,
disjoint-union-comb-single-val,
disjoint-classrel_wf,
single-valued-classrel_wf,
event-ordering+_wf,
classrel_wf,
State2_wf,
es-E_wf,
event-ordering+_subtype,
less_than_wf,
bag-size_wf,
class-ap_wf,
nat_wf,
eclass_wf,
Id_wf
Latex:
\mforall{}[Info,A1,A2,S:Type]. \mforall{}[init:Id {}\mrightarrow{} S]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} S
{}\mrightarrow{} S].
\mforall{}[X2:EClass(A2)].
\mforall{}es:EO+(Info)
(single-valued-classrel(es;X1;A1)
{}\mRightarrow{} single-valued-classrel(es;X2;A2)
{}\mRightarrow{} disjoint-classrel(es;A1;X1;A2;X2)
{}\mRightarrow{} State2(init;tr1;X1;tr2;X2) is functional)
Date html generated:
2015_07_22-PM-00_25_39
Last ObjectModification:
2015_01_28-AM-10_08_52
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