Nuprl Lemma : memory-class3-program_wf
∀[Info,A1,A2,A3,B:Type]. ∀[init:Id ─→ B]. ∀[tr1:Id ─→ A1 ─→ B ─→ B]. ∀[X1:EClass(A1)]. ∀[pr1:LocalClass(X1)].
∀[tr2:Id ─→ A2 ─→ B ─→ B]. ∀[X2:EClass(A2)]. ∀[pr2:LocalClass(X2)]. ∀[tr3:Id ─→ A3 ─→ B ─→ B]. ∀[X3:EClass(A3)].
∀[pr3:LocalClass(X3)].
  (memory-class3-program(init;tr1;pr1;tr2;pr2;tr3;pr3)
   ∈ LocalClass(memory-class3(init;tr1;X1;tr2;X2;tr3;X3))) supposing 
     (valueall-type(A1) and 
     valueall-type(A2) and 
     valueall-type(A3) and 
     valueall-type(B) and 
     (↓B))
Proof
Definitions occuring in Statement : 
memory-class3-program: memory-class3-program(init;tr1;pr1;tr2;pr2;tr3;pr3)
, 
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3)
, 
local-class: LocalClass(X)
, 
eclass: EClass(A[eo; e])
, 
Id: Id
, 
valueall-type: valueall-type(T)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
squash: ↓T
, 
member: t ∈ T
, 
function: x:A ─→ B[x]
, 
universe: Type
Lemmas : 
valueall-type_wf, 
squash_wf, 
local-class_wf, 
eclass_wf, 
es-E_wf, 
event-ordering+_subtype, 
event-ordering+_wf, 
Id_wf, 
valueall-type-value-type, 
loop-class-memory-program_wf, 
parallel-class_wf, 
eclass1_wf, 
single-bag_wf, 
parallel-class-program_wf, 
function-valueall-type, 
eclass1-program_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{}[pr1:LocalClass(X1)].  \mforall{}[tr2:Id  {}\mrightarrow{}  A2  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[X2:EClass(A2)].  \mforall{}[pr2:LocalClass(X2)].
\mforall{}[tr3:Id  {}\mrightarrow{}  A3  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[X3:EClass(A3)].  \mforall{}[pr3:LocalClass(X3)].
    (memory-class3-program(init;tr1;pr1;tr2;pr2;tr3;pr3)
      \mmember{}  LocalClass(memory-class3(init;tr1;X1;tr2;X2;tr3;X3)))  supposing 
          (valueall-type(A1)  and 
          valueall-type(A2)  and 
          valueall-type(A3)  and 
          valueall-type(B)  and 
          (\mdownarrow{}B))
Date html generated:
2015_07_22-PM-00_05_39
Last ObjectModification:
2015_01_28-AM-09_52_40
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