helm/software/matita/library/dama/models/nat_ordered_uniform.ma

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  14
  15 include "dama/models/nat_uniform.ma".
  16 include "dama/bishop_set_rewrite.ma".
  17 include "dama/ordered_uniform.ma".
  18
  19 definition nat_ordered_uniform_space:ordered_uniform_space.
  20  apply (mk_ordered_uniform_space (mk_ordered_uniform_space_ ℕ ℕ (refl_eq ? ℕ)));
  21 simplify; intros 10;  cases H (_); cases (H7 y); apply H8; cases (H7 s);
  22 lapply (H11 H1) as H13; apply (le_le_eq);
  23 [2: apply (le_transitive ??? H5); apply (Le≪ ? H13); assumption;
  24 |1: assumption;
  25 |3: change with (le (os_r ℕ) (\snd y) (\fst y));
  26     apply (ge_transitive ??? H5);apply (ge_transitive ???? H4);
  27     change with (le (os_l ℕ) (\fst s) (\snd s));
  28     apply (Le≫ ? H13); apply le_reflexive;
  29 |4: assumption;]
  30 qed.
  31
  32 interpretation "Ordered uniform space N" 'N = nat_ordered_uniform_space.