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

`∀[A:Type]`
`  ∀eq:EqDecider(A)`
`    ∀[B:A ─→ Type]`
`      ∀L:a:A fp-> B[a] List. ∀x:A.  (∃f∈L. (↑x ∈ dom(f)) ∧ (⊕(L)(x) = f(x) ∈ B[x])) supposing ↑x ∈ dom(⊕(L))`

Proof

Definitions occuring in Statement :  fpf-join-list: `⊕(L)` fpf-ap: `f(x)` 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` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` so_apply: `x[s]` all: `∀x:A. B[x]` and: `P ∧ Q` function: `x:A ─→ B[x]` universe: `Type` equal: `s = t ∈ T`
Lemmas :  fpf-join-dom fpf-join_wf subtype_top top_wf subtype-fpf2 fpf-dom_wf assert_wf l_member_wf fpf_wf l_exists_wf iff_weakening_equal fpf-ap_wf fpf-join-list_wf fpf-join-ap-left sq_stable__le select_wf assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert eqtt_to_assert bool_wf fpf-join-ap
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A  {}\mrightarrow{}  Type]
\mforall{}L:a:A  fp->  B[a]  List.  \mforall{}x:A.
(\mexists{}f\mmember{}L.  (\muparrow{}x  \mmember{}  dom(f))  \mwedge{}  (\moplus{}(L)(x)  =  f(x)))  supposing  \muparrow{}x  \mmember{}  dom(\moplus{}(L))

Date html generated: 2015_07_17-AM-09_21_01
Last ObjectModification: 2015_07_16-AM-09_51_32

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