{ [es:EO]. [R:{R:E  E  | e,e':E.  (R[e;e']  (e' < e))} ].
  [d:e,e':E.  Dec(R e e')].
    (es-r-pred{i:l}(es;d)  E  (E + Top)) }

{ Proof }



Definitions occuring in Statement :  es-r-pred: es-r-pred{i:l}(es;d) es-causl: (e < e') es-E: E event_ordering: EO decidable: Dec(P) uall: [x:A]. B[x] top: Top prop: so_apply: x[s1;s2] all: x:A. B[x] implies: P  Q member: t  T set: {x:A| B[x]}  apply: f a function: x:A  B[x] union: left + right
Definitions :  fpf: a:A fp-B[a] strong-subtype: strong-subtype(A;B) list: type List le: A  B ge: i  j  not: A less_than: a < b uimplies: b supposing a product: x:A  B[x] and: P  Q uiff: uiff(P;Q) or: P  Q eq_atom: x =a y eq_atom: eq_atom$n(x;y) record-select: r.x infix_ap: x f y dep-isect: Error :dep-isect,  record+: record+ subtype_rel: A r B axiom: Ax es-r-pred: es-r-pred{i:l}(es;d) top: Top union: left + right event_ordering: EO equal: s = t implies: P  Q es-causl: (e < e') so_apply: x[s1;s2] universe: Type set: {x:A| B[x]}  uall: [x:A]. B[x] function: x:A  B[x] decidable: Dec(P) apply: f a es-E: E prop: all: x:A. B[x] member: t  T isect: x:A. B[x] pi1: fst(t) void: Void subtype: S  T suptype: suptype(S; T) lambda: x.A[x] so_lambda: x.t[x] causal-pred-from-relation rev_implies: P  Q limited-type: LimitedType do-apply: do-apply(f;x) can-apply: can-apply(f;x) assert: b exists: x:A. B[x] iff: P  Q causal-predecessor: causal-predecessor(es;p) Auto: Error :Auto,  Unfold: Error :Unfold,  CollapseTHEN: Error :CollapseTHEN,  tactic: Error :tactic
Lemmas :  causal-predecessor_wf iff_wf assert_wf uall_wf causal-pred-from-relation can-apply_wf do-apply_wf subtype_rel_wf pi1_wf_top member_wf top_wf decidable_wf es-E_wf es-causl_wf event_ordering_wf

\mforall{}[es:EO].  \mforall{}[R:\{R:E  {}\mrightarrow{}  E  {}\mrightarrow{}  \mBbbP{}|  \mforall{}e,e':E.    (R[e;e']  {}\mRightarrow{}  (e'  <  e))\}  ].  \mforall{}[d:\mforall{}e,e':E.    Dec(R  e  e')].
    (es-r-pred\{i:l\}(es;d)  \mmember{}  E  {}\mrightarrow{}  (E  +  Top))


Date html generated: 2011_08_16-AM-11_13_13
Last ObjectModification: 2011_06_20-AM-00_20_42

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