matita/matita/contribs/lambdadelta/ground_2/relocation/trace_sor.ma

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  14
  15 include "ground_2/notation/relations/runion_3.ma".
  16 include "ground_2/relocation/trace.ma".
  17
  18 (* RELOCATION TRACE *********************************************************)
  19
  20 inductive sor: relation3 trace trace trace ≝
  21    | sor_empty: sor (◊) (◊) (◊)
  22    | sor_inh  : ∀cs1,cs2,cs. sor cs1 cs2 cs →
  23                 ∀b1,b2. sor (b1 @ cs1) (b2 @ cs2) ((b1 ∨ b2) @ cs).
  24
  25 interpretation
  26    "union (trace)"
  27    'RUnion L1 L2 L = (sor L2 L1 L).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma sor_sym: ∀cs1,cs2,cs. cs1 ⋓ cs2 ≡ cs → cs2 ⋓ cs1 ≡ cs.
  32 #cs1 #cs2 #cs #H elim H -cs1 -cs2 -cs /2 width=1 by sor_inh/
  33 qed-.