{ es:EO
    [P:E  ]
      d:e,e':E.  Dec(es-p-immediate-pred(es;e.P[e]) e e')
        ((e:E. Dec(P[e]))
         SWellFounded(p-graph(E;es-r-pred{i:l}(es;d)) y x)) }

{ Proof }



Definitions occuring in Statement :  es-p-immediate-pred: es-p-immediate-pred(es;P) es-r-pred: es-r-pred{i:l}(es;d) es-E: E event_ordering: EO decidable: Dec(P) uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] implies: P  Q apply: f a lambda: x.A[x] function: x:A  B[x] p-graph: p-graph(A;f) strongwellfounded: SWellFounded(R[x; y])
Definitions :  subtype: S  T suptype: suptype(S; T) top: Top so_lambda: x.t[x] axiom: Ax pair: <a, b> void: Void false: False true: True decide: case b of inl(x) =s[x] | inr(y) =t[y] ifthenelse: if b then t else f fi  do-apply: do-apply(f;x) can-apply: can-apply(f;x) cand: A c B assert: b rel_implies: R1 =R2 record: record(x.T[x]) strong-subtype: strong-subtype(A;B) equal: s = t 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+ le: A  B ge: i  j  not: A uimplies: b supposing a and: P  Q uiff: uiff(P;Q) subtype_rel: A r B less_than: a < b es-r-pred: es-r-pred{i:l}(es;d) p-graph: p-graph(A;f) event_ordering: EO uall: [x:A]. B[x] isect: x:A. B[x] universe: Type apply: f a exists: x:A. B[x] product: x:A  B[x] nat: decidable: Dec(P) or: P  Q union: left + right strongwellfounded: SWellFounded(R[x; y]) es-causl: (e < e') so_lambda: x y.t[x; y] so_apply: x[s] lambda: x.A[x] es-p-immediate-pred: es-p-immediate-pred(es;P) so_apply: x[s1;s2] implies: P  Q es-E: E all: x:A. B[x] prop: function: x:A  B[x] set: {x:A| B[x]}  member: t  T guard: {T} rev_implies: P  Q iff: P  Q causal-predecessor: causal-predecessor(es;p) sq_type: SQType(T) Auto: Error :Auto,  RepUR: Error :RepUR,  CollapseTHEN: Error :CollapseTHEN,  MaAuto: Error :MaAuto,  AssertBY: Error :AssertBY,  HypSubst: Error :HypSubst,  CollapseTHENA: Error :CollapseTHENA
Lemmas :  es-r-pred-property subtype_base_sq es-E_wf strongwf-monotone es-causl_wf p-graph_wf es-r-pred_wf es-p-immediate-pred_wf event_ordering_wf decidable_wf nat_wf strongwellfounded_wf p-graph_wf2 rel_implies_wf assert_wf pair_wf assert_witness can-apply_wf top_wf member_wf do-apply_wf es-causl-swellfnd

\mforall{}es:EO
    \mforall{}[P:E  {}\mrightarrow{}  \mBbbP{}]
        \mforall{}d:\mforall{}e,e':E.    Dec(es-p-immediate-pred(es;\mlambda{}e.P[e])  e  e')
            ((\mforall{}e:E.  Dec(P[e]))  {}\mRightarrow{}  SWellFounded(p-graph(E;es-r-pred\{i:l\}(es;d))  y  x))


Date html generated: 2011_08_16-AM-11_13_45
Last ObjectModification: 2011_06_20-AM-00_21_07

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