Nuprl Lemma : state-class5-program_wf
∀[Info,A1,A2,A3,A4,A5,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)]. ∀[tr5:Id ⟶ A5 ⟶ B ⟶ B].
∀[X5:EClass(A5)]. ∀[pr5:LocalClass(X5)].
(state-class5-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4;tr5;pr5)
∈ LocalClass(state-class5(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4;tr5;X5))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(A3) and
valueall-type(A4) and
valueall-type(A5) and
valueall-type(B) and
(↓B))
Proof
Definitions occuring in Statement :
state-class5-program: state-class5-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4;tr5;pr5),
state-class5: state-class5(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4;tr5;X5),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
state-class5-program: state-class5-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4;tr5;pr5),
state-class5: state-class5(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4;tr5;X5),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info,A1,A2,A3,A4,A5,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)]. \mforall{}[tr5:Id {}\mrightarrow{} A5 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X5:EClass(A5)].
\mforall{}[pr5:LocalClass(X5)].
(state-class5-program(init;tr1;pr1;tr2;pr2;tr3;pr3;tr4;pr4;tr5;pr5)
\mmember{} LocalClass(state-class5(init;tr1;X1;tr2;X2;tr3;X3;tr4;X4;tr5;X5))) supposing
(valueall-type(A1) and
valueall-type(A2) and
valueall-type(A3) and
valueall-type(A4) and
valueall-type(A5) and
valueall-type(B) and
(\mdownarrow{}B))
Date html generated:
2016_05_17-AM-09_11_32
Last ObjectModification:
2016_01_17-PM-09_14_08
Theory : local!classes
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