---

{ [A:Type]
    eq:EqDecider(A). f,g:a:A fp-> Top. x:A. R:Top.
      (x  dom(fpf-union-join(eq;R;f;g))  (x  dom(f))  (x  dom(g))) }

{ Proof }

---

Definitions occuring in Statement :  fpf-union-join: fpf-union-join(eq;R;f;g),  fpf-dom: x  dom(f),  fpf: a:A fp-> B[a],  assert: b,  uall: [x:A]. B[x],  top: Top,  all: x:A. B[x],  iff: P  Q,  or: P  Q,  universe: Type,  deq: EqDecider(T)
Definitions :  uall: [x:A]. B[x],  all: x:A. B[x],  member: t  T,  so_lambda: x.t[x],  iff: P  Q,  fpf-dom: x  dom(f),  fpf-union-join: fpf-union-join(eq;R;f;g),  or: P  Q,  pi1: fst(t),  prop: ,  and: P  Q,  implies: P  Q,  rev_implies: P  Q,  so_apply: x[s],  fpf: a:A fp-> B[a],  decidable: Dec(P),  not: A,  uimplies: b supposing a,  false: False
Lemmas :  top_wf,  fpf_wf,  deq_wf,  assert_wf,  deq-member_wf,  append_wf,  filter_wf,  bnot_wf,  l_member_wf,  iff_functionality_wrt_iff,  or_functionality_wrt_iff,  member_filter,  assert-deq-member,  member_append,  decidable__assert,  not_functionality_wrt_iff,  not_wf,  and_functionality_wrt_iff,  iff_transitivity,  iff_weakening_uiff,  assert_of_bnot

---

\mforall{}[A:Type]
    \mforall{}eq:EqDecider(A).  \mforall{}f,g:a:A  fp->  Top.  \mforall{}x:A.  \mforall{}R:Top.
        (\muparrow{}x  \mmember{}  dom(fpf-union-join(eq;R;f;g))  \mLeftarrow{}{}\mRightarrow{}  (\muparrow{}x  \mmember{}  dom(f))  \mvee{}  (\muparrow{}x  \mmember{}  dom(g)))


Date html generated: 2011_08_10-AM-08_01_39
Last ObjectModification: 2011_06_18-AM-08_20_05

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