Nuprl Lemma : state-class4_wf
∀[Info,A1,A2,A3,A4,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)]. ∀[tr4:Id ⟶ A4 ⟶ B ⟶ B]. ∀[X4:EClass(A4)].
(state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4) ∈ EClass(B))
Proof
Definitions occuring in Statement :
state-class4: state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
state-class4: state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4),
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
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{}[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{}[tr4:Id {}\mrightarrow{} A4 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X4:EClass(A4)].
(state-class4(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4) \mmember{} EClass(B))
Date html generated:
2016_05_16-PM-11_44_21
Last ObjectModification:
2015_12_29-AM-10_05_06
Theory : event-ordering
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