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

`∀[A:Type]. ∀eq:EqDecider(A). ∀[B:A ─→ Type]. ∀L:a:A fp-> B[a] 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]` so_apply: `x[s]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` function: `x:A ─→ B[x]` universe: `Type`
Lemmas :  list_induction all_wf iff_wf assert_wf fpf-dom_wf fpf-join-list_wf top_wf subtype_rel_list fpf_wf subtype-fpf2 subtype_top l_exists_wf l_member_wf list_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-dom fpf-join_wf
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}L:a:A  fp->  B[a]  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_50
Last ObjectModification: 2015_01_28-AM-07_49_20

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