### Nuprl Lemma : disjoint-union-comb-classrel-weak

`∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].`
`  ∀v:A + B. (v ∈ X (+) Y(e) `⇐⇒` ((↑isl(v)) ∧ outl(v) ∈ X(e)) ∨ ((¬↑isl(v)) ∧ outr(v) ∈ Y(e)))`

Proof

Definitions occuring in Statement :  disjoint-union-comb: `X (+) Y` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` outr: `outr(x)` outl: `outl(x)` assert: `↑b` isl: `isl(x)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` not: `¬A` or: `P ∨ Q` and: `P ∧ Q` union: `left + right` universe: `Type`
Lemmas :  disjoint-union-comb-classrel classrel_wf disjoint-union-comb_wf or_wf assert_wf isl_wf not_wf not_assert_elim btrue_wf btrue_neq_bfalse es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf

Latex:
\mforall{}[Info,A,B:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}v:A  +  B.  (v  \mmember{}  X  (+)  Y(e)  \mLeftarrow{}{}\mRightarrow{}  ((\muparrow{}isl(v))  \mwedge{}  outl(v)  \mmember{}  X(e))  \mvee{}  ((\mneg{}\muparrow{}isl(v))  \mwedge{}  outr(v)  \mmember{}  Y(e)))

Date html generated: 2015_07_22-PM-00_19_19
Last ObjectModification: 2015_01_28-AM-10_42_20

Home Index