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

`∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].`
`  ∀v:A + B. uiff(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)` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` not: `¬A` or: `P ∨ Q` and: `P ∧ Q` union: `left + right` universe: `Type`
Lemmas :  parallel-classrel simple-comb-1_wf lifting-1_wf simple-comb-1-classrel and_wf equal_wf isl_wf btrue_wf subtype_base_sq bool_wf bool_subtype_base outl_wf assert_wf classrel_wf not_wf not_assert_elim btrue_neq_bfalse assert_elim bfalse_wf outr_wf squash_wf bnot_wf assert_of_bnot sq_stable__classrel true_wf false_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.  uiff(v  \mmember{}  X  (+)  Y(e);((\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_17
Last ObjectModification: 2015_01_28-AM-10_45_57

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