src/HOL/Nat.ML
changeset 1485 240cc98b94a7
parent 1475 7f5a4cd08209
child 1531 e5eb247ad13c
equal deleted inserted replaced
1484:b43cd8a8061f 1485:240cc98b94a7
   341 
   341 
   342 goal Nat.thy "!!i. i<j ==> j<k --> Suc i < k";
   342 goal Nat.thy "!!i. i<j ==> j<k --> Suc i < k";
   343 by(nat_ind_tac "k" 1);
   343 by(nat_ind_tac "k" 1);
   344 by(ALLGOALS (asm_simp_tac (!simpset addsimps [less_Suc_eq])));
   344 by(ALLGOALS (asm_simp_tac (!simpset addsimps [less_Suc_eq])));
   345 by(fast_tac (HOL_cs addDs [Suc_lessD]) 1);
   345 by(fast_tac (HOL_cs addDs [Suc_lessD]) 1);
   346 bind_thm("less_trans_Suc",result() RS mp);
   346 qed_spec_mp "less_trans_Suc";
   347 
   347 
   348 (*"Less than" is a linear ordering*)
   348 (*"Less than" is a linear ordering*)
   349 goal Nat.thy "m<n | m=n | n<(m::nat)";
   349 goal Nat.thy "m<n | m=n | n<(m::nat)";
   350 by (nat_ind_tac "m" 1);
   350 by (nat_ind_tac "m" 1);
   351 by (nat_ind_tac "n" 1);
   351 by (nat_ind_tac "n" 1);