Nuprl Lemma : Accum-class-single-val
∀[Info,A,B:Type]. ∀[es:EO+(Info)].
∀X:EClass(A)
∀[init:Id ⟶ bag(B)]. ∀[f:A ⟶ B ⟶ B].
(single-valued-classrel(es;X;A)
⇒ (∀l:Id. single-valued-bag(init l;B))
⇒ single-valued-classrel(es;Accum-class(f;init;X);B))
Proof
Definitions occuring in Statement :
Accum-class: Accum-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 :
Accum-class: Accum-class(f;init;X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)].
\mforall{}X:EClass(A)
\mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B].
(single-valued-classrel(es;X;A)
{}\mRightarrow{} (\mforall{}l:Id. single-valued-bag(init l;B))
{}\mRightarrow{} single-valued-classrel(es;Accum-class(f;init;X);B))
Date html generated:
2016_05_17-AM-09_31_46
Last ObjectModification:
2015_12_29-PM-04_00_36
Theory : classrel!lemmas
Home
Index