Nuprl Lemma : disjoint-union-classrel-ite-weak

[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A B].
  (v ∈ 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: 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: ⇐⇒ Q not: ¬A squash: T or: P ∨ Q and: P ∧ Q union: left right universe: Type
Lemmas :  disjoint-union-classrel-ite 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

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{}  \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_29
Last ObjectModification: 2015_01_28-AM-10_45_50

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