src/HOL/Presburger.thy

changeset 35216 | 7641e8d831d2 |

parent 35050 | 9f841f20dca6 |

child 36749 | a8dc19a352e6 |

--- a/src/HOL/Presburger.thy Thu Feb 18 13:29:59 2010 -0800 +++ b/src/HOL/Presburger.thy Thu Feb 18 14:21:44 2010 -0800 @@ -199,16 +199,16 @@ hence "P 0" using P Pmod by simp moreover have "P 0 = P(0 - (-1)*d)" using modd by blast ultimately have "P d" by simp - moreover have "d : {1..d}" using dpos by(simp add:atLeastAtMost_iff) + moreover have "d : {1..d}" using dpos by simp ultimately show ?RHS .. next assume not0: "x mod d \<noteq> 0" - have "P(x mod d)" using dpos P Pmod by(simp add:pos_mod_sign pos_mod_bound) + have "P(x mod d)" using dpos P Pmod by simp moreover have "x mod d : {1..d}" proof - from dpos have "0 \<le> x mod d" by(rule pos_mod_sign) moreover from dpos have "x mod d < d" by(rule pos_mod_bound) - ultimately show ?thesis using not0 by(simp add:atLeastAtMost_iff) + ultimately show ?thesis using not0 by simp qed ultimately show ?RHS .. qed