Nuprl Lemma : Memory-class-single-val
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)].
∀es:EO+(Info)
(single-valued-classrel(es;X;A)
⇒ (∀l:Id. single-valued-bag(init l;S))
⇒ single-valued-classrel(es;Memory-class(f;init;X);S))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
single-valued-classrel: single-valued-classrel(es;X;T),
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
or: P ∨ Q,
not: ¬A,
false: False,
guard: {T},
single-valued-bag: single-valued-bag(b;T)
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)].
\mforall{}es:EO+(Info)
(single-valued-classrel(es;X;A)
{}\mRightarrow{} (\mforall{}l:Id. single-valued-bag(init l;S))
{}\mRightarrow{} single-valued-classrel(es;Memory-class(f;init;X);S))
Date html generated:
2016_05_17-AM-09_23_36
Last ObjectModification:
2015_12_29-PM-04_05_51
Theory : classrel!lemmas
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