Nuprl Lemma : state-class4-program_wf
∀[Info,A1,A2,A3,A4,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)]. ∀[tr4:Id ─→ A4 ─→ B ─→ B]. ∀[X4:EClass(A4)]. ∀[pr4:LocalClass(X4)].
(state-class4-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4)
∈ LocalClass(state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(A3) and
valueall-type(A4) and
valueall-type(B) and
(↓B))
Proof
Definitions occuring in Statement :
state-class4-program: state-class4-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4),
state-class4: state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4),
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,A3,A4,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)]. \mforall{}[tr4:Id {}\mrightarrow{} A4 {}\mrightarrow{} B {}\mrightarrow{} B].
\mforall{}[X4:EClass(A4)]. \mforall{}[pr4:LocalClass(X4)].
(state-class4-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4)
\mmember{} LocalClass(state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(A3) and
valueall-type(A4) and
valueall-type(B) and
(\mdownarrow{}B))
Date html generated:
2015_07_22-PM-00_05_22
Last ObjectModification:
2015_01_28-AM-09_53_01
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