Nuprl Lemma : locl-pre-preserving-compose

es:EO
  ∀[P,Q:E ─→ ℙ].
    ∀f1:{e:E| e}  ─→ {e:E| e} . ∀f2:{e:E| e}  ─→ E.
      ((f1 is locl-pre-preserving on P ∧ f2 is locl-pre-preserving on Q)  f2 f1 is locl-pre-preserving on P)


Proof




Definitions occuring in Statement :  locl-pre-preserving: is locl-pre-preserving on P es-E: E event_ordering: EO compose: g uall: [x:A]. B[x] prop: all: x:A. B[x] implies:  Q and: P ∧ Q set: {x:A| B[x]}  apply: a function: x:A ─→ B[x]
Lemmas :  locl-pre-preserving_wf subtype_rel_dep_function es-E_wf set_wf event_ordering_wf rel-pre-preserving-compose es-le_wf
\mforall{}es:EO
    \mforall{}[P,Q:E  {}\mrightarrow{}  \mBbbP{}].
        \mforall{}f1:\{e:E|  P  e\}    {}\mrightarrow{}  \{e:E|  Q  e\}  .  \mforall{}f2:\{e:E|  Q  e\}    {}\mrightarrow{}  E.
            ((f1  is  locl-pre-preserving  on  P  \mwedge{}  f2  is  locl-pre-preserving  on  Q)
            {}\mRightarrow{}  f2  o  f1  is  locl-pre-preserving  on  P)



Date html generated: 2015_07_17-AM-09_03_51
Last ObjectModification: 2015_01_27-PM-00_52_24

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