### Nuprl Lemma : fpf-join-list-dom2

`∀[A:Type]. ∀eq:EqDecider(A). ∀L:a:A fp-> Top List. ∀x:A.  (↑x ∈ dom(⊕(L)) `⇐⇒` (∃f∈L. ↑x ∈ dom(f)))`

Proof

Definitions occuring in Statement :  fpf-join-list: `⊕(L)` fpf-dom: `x ∈ dom(f)` fpf: `a:A fp-> B[a]` deq: `EqDecider(T)` l_exists: `(∃x∈L. P[x])` list: `T List` assert: `↑b` uall: `∀[x:A]. B[x]` top: `Top` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` universe: `Type`
Lemmas :  list_induction all_wf iff_wf assert_wf fpf-dom_wf fpf-join-list_wf top_wf l_exists_wf l_member_wf list_wf fpf_wf deq_wf reduce_nil_lemma deq_member_nil_lemma false_wf l_exists_nil l_exists_wf_nil l_exists_cons cons_wf or_wf reduce_cons_lemma fpf-join-list-dom fpf-join-dom fpf-join_wf
\mforall{}[A:Type].  \mforall{}eq:EqDecider(A).  \mforall{}L:a:A  fp->  Top  List.  \mforall{}x:A.    (\muparrow{}x  \mmember{}  dom(\moplus{}(L))  \mLeftarrow{}{}\mRightarrow{}  (\mexists{}f\mmember{}L.  \muparrow{}x  \mmember{}  dom(f)))

Date html generated: 2015_07_17-AM-09_20_53
Last ObjectModification: 2015_01_28-AM-07_47_41

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