Nuprl Lemma : state-class1-state1-classrel
∀[Info,B,A:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ B]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
uiff(v ∈ State1(init;f;X)(e);v ∈ state-class1(init;f;X)(e))
Proof
Definitions occuring in Statement :
State1: State1(init;tr;X),
state-class1: state-class1(init;tr;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:B].
uiff(v \mmember{} State1(init;f;X)(e);v \mmember{} state-class1(init;f;X)(e))
Date html generated:
2016_05_17-AM-10_04_44
Last ObjectModification:
2016_01_17-PM-11_02_32
Theory : classrel!lemmas
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