Nuprl Lemma : Accum-class-es-sv1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(B)]. ∀[f:A ⟶ B ⟶ B].
(es-sv-class(es;Accum-class(f;init;X))) supposing ((∀l:Id. (#(init l) ≤ 1)) and es-sv-class(es;X))
Proof
Definitions occuring in Statement :
Accum-class: Accum-class(f;init;X),
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
Accum-class: Accum-class(f;init;X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
nat: ℕ,
prop: ℙ,
es-sv-class: es-sv-class(es;X),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False
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].
(es-sv-class(es;Accum-class(f;init;X))) supposing ((\mforall{}l:Id. (\#(init l) \mleq{} 1)) and es-sv-class(es;X))
Date html generated:
2016_05_17-AM-09_31_57
Last ObjectModification:
2015_12_29-PM-04_00_54
Theory : classrel!lemmas
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