Nuprl Lemma : eclass0-single-val
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ⟶ B ⟶ bag(C)]. ∀[es:EO+(Info)].
(single-valued-classrel(es;(f o X);C)) supposing
(single-valued-classrel(es;X;B) and
(∀i:Id. ∀b:B. single-valued-bag(f i b;C)))
Proof
Definitions occuring in Statement :
eclass0: (f o X),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
squash: ↓T,
exists: ∃x:A. B[x],
classrel: v ∈ X(e),
single-valued-bag: single-valued-bag(b;T)
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[es:EO+(Info)].
(single-valued-classrel(es;(f o X);C)) supposing
(single-valued-classrel(es;X;B) and
(\mforall{}i:Id. \mforall{}b:B. single-valued-bag(f i b;C)))
Date html generated:
2016_05_16-PM-02_09_14
Last ObjectModification:
2015_12_29-PM-02_27_35
Theory : event-ordering
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