Nuprl Lemma : state-class2-program_wf
∀[Info,A1,A2,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)].
(state-class2-program(init;tr1;pr1;tr2;pr2) ∈ LocalClass(state-class2(init;tr1;X1;tr2;X2))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(B) and
(↓B))
Proof
Definitions occuring in Statement :
state-class2-program: state-class2-program(init;tr1;pr1;tr2;pr2),
state-class2: state-class2(init;tr1;X1;tr2;X2),
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-state-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,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)].
(state-class2-program(init;tr1;pr1;tr2;pr2)
\mmember{} LocalClass(state-class2(init;tr1;X1;tr2;X2))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(B) and
(\mdownarrow{}B))
Date html generated:
2015_07_22-PM-00_05_13
Last ObjectModification:
2015_01_28-AM-09_52_42
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