Nuprl Lemma : disjoint-union-class-single-val
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
(single-valued-classrel(es;X;A) ⇒ single-valued-classrel(es;Y;B) ⇒ single-valued-classrel(es;X + Y;A + B))
Proof
Definitions occuring in Statement :
disjoint-union-class: X + Y,
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
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],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
not: ¬A,
false: False
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-classrel(es;Y;B)
{}\mRightarrow{} single-valued-classrel(es;X + Y;A + B))
Date html generated:
2016_05_17-AM-09_28_44
Last ObjectModification:
2015_12_29-PM-04_02_15
Theory : classrel!lemmas
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