Nuprl Lemma : primed-class-opt-single-val
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ⟶ bag(B)].
((∀l:Id. single-valued-bag(init l;B)) ⇒ single-valued-classrel(es;X;B) ⇒ single-valued-classrel(es;Prior(X)?init;B))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀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],
guard: {T}
Latex:
\mforall{}[Info,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
((\mforall{}l:Id. single-valued-bag(init l;B))
{}\mRightarrow{} single-valued-classrel(es;X;B)
{}\mRightarrow{} single-valued-classrel(es;Prior(X)?init;B))
Date html generated:
2016_05_17-AM-09_16_21
Last ObjectModification:
2015_12_29-PM-04_09_30
Theory : classrel!lemmas
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