Nuprl Lemma : cut-order-induction

[Info:Type]
  ∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X).
    ∀[P:E(X) ─→ ℙ]. ((∀b:E(X). ((∀a:E(X). (P[a]) supposing ((¬(a b ∈ E(X))) and a ≤(X;f) b))  P[b]))  (∀e:E(X). P[\000Ce]))


Proof




Definitions occuring in Statement :  cut-order: a ≤(X;f) b sys-antecedent: sys-antecedent(es;Sys) es-E-interface: E(X) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) uimplies: supposing a uall: [x:A]. B[x] top: Top prop: so_apply: x[s] all: x:A. B[x] not: ¬A implies:  Q function: x:A ─→ B[x] universe: Type equal: t ∈ T
Lemmas :  es-causl-swellfnd event-ordering+_subtype less_than_transitivity1 less_than_irreflexivity int_seg_wf decidable__equal_int subtype_rel-int_seg false_wf le_weakening subtract_wf int_seg_properties le_wf nat_wf zero-le-nat lelt_wf es-causl_wf cut-order_witness not_wf equal_wf cut-order_wf all_wf int_seg_subtype-nat decidable__lt not-equal-2 condition-implies-le minus-add minus-minus minus-one-mul add-swap add-commutes add-associates add_functionality_wrt_le zero-add le-add-cancel-alt less-iff-le le-add-cancel set_wf less_than_wf primrec-wf2 decidable__le not-le-2 sq_stable__le add-zero add-mul-special zero-mul es-E-interface_wf isect_wf sys-antecedent_wf eclass_wf top_wf es-E_wf event-ordering+_wf cut-order-causle assert_elim in-eclass_wf subtype_base_sq bool_wf bool_subtype_base assert_wf

Latex:
\mforall{}[Info:Type]
    \mforall{}es:EO+(Info).  \mforall{}X:EClass(Top).  \mforall{}f:sys-antecedent(es;X).
        \mforall{}[P:E(X)  {}\mrightarrow{}  \mBbbP{}]
            ((\mforall{}b:E(X).  ((\mforall{}a:E(X).  (P[a])  supposing  ((\mneg{}(a  =  b))  and  a  \mleq{}(X;f)  b))  {}\mRightarrow{}  P[b]))  {}\mRightarrow{}  (\mforall{}e:E(X).  P[e\000C]))



Date html generated: 2015_07_21-PM-04_06_13
Last ObjectModification: 2015_01_27-PM-05_47_26

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