Nuprl Lemma : iseg-local-relation

[Info:Type]
  ∀L1,L2:(Id × Info) List.
    (L1 ≤ L2
     (∀[R:Id ⟶ Id ⟶ Info List+ ⟶ Info List+ ⟶ ℙ]
          ∀e1,e2:E.
            (es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L1);e1;e2)
            ⇐⇒ es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L2);e1;e2))))


Proof




Definitions occuring in Statement :  global-eo: global-eo(L) es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2) es-E: E Id: Id iseg: l1 ≤ l2 listp: List+ list: List uall: [x:A]. B[x] prop: so_apply: x[s1;s2;s3;s4] all: x:A. B[x] iff: ⇐⇒ Q implies:  Q function: x:A ⟶ B[x] product: x:A × B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] implies:  Q subtype_rel: A ⊆B prop: uimplies: supposing a top: Top int_seg: {i..j-} lelt: i ≤ j < k and: P ∧ Q iff: ⇐⇒ Q rev_implies:  Q decidable: Dec(P) or: P ∨ Q less_than: a < b squash: T le: A ≤ B satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A true: True es-embedding: (f embeds eo1 into eo2)

Latex:
\mforall{}[Info:Type]
    \mforall{}L1,L2:(Id  \mtimes{}  Info)  List.
        (L1  \mleq{}  L2
        {}\mRightarrow{}  (\mforall{}[R:Id  {}\mrightarrow{}  Id  {}\mrightarrow{}  Info  List\msupplus{}  {}\mrightarrow{}  Info  List\msupplus{}  {}\mrightarrow{}  \mBbbP{}]
                    \mforall{}e1,e2:E.
                        (es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L1);e1;e2)
                        \mLeftarrow{}{}\mRightarrow{}  es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L2);e1;e2))))



Date html generated: 2016_05_17-AM-08_34_23
Last ObjectModification: 2016_01_17-PM-02_27_37

Theory : event-ordering


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