Nuprl Lemma : disjoint-union-classrel-ite

`∀[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) ∧ (∀w:A. (¬w ∈ X(e)))))`

Proof

Definitions occuring in Statement :  disjoint-union-class: `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` squash: `↓T` or: `P ∨ Q` and: `P ∧ Q` union: `left + right` universe: `Type`
Lemmas :  classrel_wf disjoint-union-class_wf squash_wf or_wf assert_wf isl_wf not_wf not_assert_elim btrue_wf btrue_neq_bfalse all_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf true_wf false_wf iff_weakening_uiff disjoint-union-classrel uiff_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);\mdownarrow{}((\muparrow{}isl(v))  \mwedge{}  outl(v)  \mmember{}  X(e))
\mvee{}  ((\mneg{}\muparrow{}isl(v))  \mwedge{}  outr(v)  \mmember{}  Y(e)  \mwedge{}  (\mforall{}w:A.  (\mneg{}w  \mmember{}  X(e)))))

Date html generated: 2015_07_22-PM-00_14_26
Last ObjectModification: 2015_01_28-AM-10_46_19

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