Nuprl Lemma : memory-class3-functional
∀[Info,A1,A2,A3,B:Type]. ∀[init:Id ─→ B]. ∀[tr1:Id ─→ A1 ─→ B ─→ B]. ∀[X1:EClass(A1)]. ∀[tr2:Id ─→ A2 ─→ B ─→ B].
∀[X2:EClass(A2)]. ∀[tr3:Id ─→ A3 ─→ B ─→ B]. ∀[X3:EClass(A3)]. ∀[es:EO+(Info)].
(memory-class3(init;tr1;X1;tr2;X2;tr3;X3) is functional) supposing
(single-valued-classrel(es;X1;A1) and
single-valued-classrel(es;X2;A2) and
single-valued-classrel(es;X3;A3) and
disjoint-classrel(es;A1;X1;A2;X2) and
disjoint-classrel(es;A1;X1;A3;X3) and
disjoint-classrel(es;A2;X2;A3;X3))
Proof
Definitions occuring in Statement :
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3),
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
loop-class-memory-functional,
single-bag_wf,
parallel-class_wf,
eclass1_wf,
bag_size_single_lemma,
false_wf,
parallel-class-single-val,
eclass1-disjoint-classrel,
disjoint-classrel-symm,
parallel-class-disjoint-classrel,
eclass1-single-val,
single-valued-bag-single,
classrel_wf,
memory-class3_wf,
es-E_wf,
event-ordering+_subtype,
less_than_wf,
bag-size_wf,
class-ap_wf,
nat_wf,
single-valued-classrel_wf,
disjoint-classrel_wf,
event-ordering+_wf,
eclass_wf,
Id_wf
Latex:
\mforall{}[Info,A1,A2,A3,B:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} B
{}\mrightarrow{} B].
\mforall{}[X2:EClass(A2)]. \mforall{}[tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X3:EClass(A3)]. \mforall{}[es:EO+(Info)].
(memory-class3(init;tr1;X1;tr2;X2;tr3;X3) is functional) supposing
(single-valued-classrel(es;X1;A1) and
single-valued-classrel(es;X2;A2) and
single-valued-classrel(es;X3;A3) and
disjoint-classrel(es;A1;X1;A2;X2) and
disjoint-classrel(es;A1;X1;A3;X3) and
disjoint-classrel(es;A2;X2;A3;X3))
Date html generated:
2015_07_22-PM-00_26_55
Last ObjectModification:
2015_01_28-AM-10_09_07
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