{ [A:Type]. [eq:EqDecider(A)]. [f,g:a:A fp-Top]. [x:A].
    (x  dom(f  g) ~ x  dom(f) x  dom(g)) }

{ Proof }



Definitions occuring in Statement :  fpf-join: f  g fpf-dom: x  dom(f) fpf: a:A fp-B[a] bor: p q uall: [x:A]. B[x] top: Top universe: Type sqequal: s ~ t deq: EqDecider(T)
Definitions :  uall: [x:A]. B[x] bor: p q member: t  T all: x:A. B[x] implies: P  Q btrue: tt assert: b prop: ifthenelse: if b then t else f fi  so_lambda: x.t[x] or: P  Q guard: {T} true: True bfalse: ff not: A sq_type: SQType(T) bool: uimplies: b supposing a unit: Unit iff: P  Q and: P  Q rev_implies: P  Q so_apply: x[s] false: False it:
Lemmas :  subtype_base_sq bool_wf bool_subtype_base fpf-dom_wf iff_weakening_uiff assert_wf eqtt_to_assert fpf-join_wf top_wf btrue_wf fpf-join-dom not_wf uiff_transitivity bnot_wf eqff_to_assert assert_of_bnot fpf_wf deq_wf assert_elim bfalse_wf not_functionality_wrt_iff

\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[f,g:a:A  fp->  Top].  \mforall{}[x:A].
    (x  \mmember{}  dom(f  \moplus{}  g)  \msim{}  x  \mmember{}  dom(f)  \mvee{}\msubb{}x  \mmember{}  dom(g))


Date html generated: 2011_08_10-AM-07_59_27
Last ObjectModification: 2011_06_18-AM-08_18_59

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