diff -r 82dd239e0f65 -r 8b1c0d434824 src/HOL/Presburger.thy --- a/src/HOL/Presburger.thy Tue Jan 15 16:19:21 2008 +0100 +++ b/src/HOL/Presburger.thy Tue Jan 15 16:19:23 2008 +0100 @@ -496,53 +496,53 @@ *} lemma eq_Pls_Pls: - "Numeral.Pls = Numeral.Pls \ True" by presburger + "Int.Pls = Int.Pls \ True" by presburger lemma eq_Pls_Min: - "Numeral.Pls = Numeral.Min \ False" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Pls = Int.Min \ False" + unfolding Pls_def Int.Min_def by presburger lemma eq_Pls_Bit0: - "Numeral.Pls = Numeral.Bit k bit.B0 \ Numeral.Pls = k" + "Int.Pls = Int.Bit k bit.B0 \ Int.Pls = k" unfolding Pls_def Bit_def bit.cases by presburger lemma eq_Pls_Bit1: - "Numeral.Pls = Numeral.Bit k bit.B1 \ False" + "Int.Pls = Int.Bit k bit.B1 \ False" unfolding Pls_def Bit_def bit.cases by presburger lemma eq_Min_Pls: - "Numeral.Min = Numeral.Pls \ False" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Min = Int.Pls \ False" + unfolding Pls_def Int.Min_def by presburger lemma eq_Min_Min: - "Numeral.Min = Numeral.Min \ True" by presburger + "Int.Min = Int.Min \ True" by presburger lemma eq_Min_Bit0: - "Numeral.Min = Numeral.Bit k bit.B0 \ False" - unfolding Numeral.Min_def Bit_def bit.cases by presburger + "Int.Min = Int.Bit k bit.B0 \ False" + unfolding Int.Min_def Bit_def bit.cases by presburger lemma eq_Min_Bit1: - "Numeral.Min = Numeral.Bit k bit.B1 \ Numeral.Min = k" - unfolding Numeral.Min_def Bit_def bit.cases by presburger + "Int.Min = Int.Bit k bit.B1 \ Int.Min = k" + unfolding Int.Min_def Bit_def bit.cases by presburger lemma eq_Bit0_Pls: - "Numeral.Bit k bit.B0 = Numeral.Pls \ Numeral.Pls = k" + "Int.Bit k bit.B0 = Int.Pls \ Int.Pls = k" unfolding Pls_def Bit_def bit.cases by presburger lemma eq_Bit1_Pls: - "Numeral.Bit k bit.B1 = Numeral.Pls \ False" + "Int.Bit k bit.B1 = Int.Pls \ False" unfolding Pls_def Bit_def bit.cases by presburger lemma eq_Bit0_Min: - "Numeral.Bit k bit.B0 = Numeral.Min \ False" - unfolding Numeral.Min_def Bit_def bit.cases by presburger + "Int.Bit k bit.B0 = Int.Min \ False" + unfolding Int.Min_def Bit_def bit.cases by presburger lemma eq_Bit1_Min: - "(Numeral.Bit k bit.B1) = Numeral.Min \ Numeral.Min = k" - unfolding Numeral.Min_def Bit_def bit.cases by presburger + "(Int.Bit k bit.B1) = Int.Min \ Int.Min = k" + unfolding Int.Min_def Bit_def bit.cases by presburger lemma eq_Bit_Bit: - "Numeral.Bit k1 v1 = Numeral.Bit k2 v2 \ + "Int.Bit k1 v1 = Int.Bit k2 v2 \ v1 = v2 \ k1 = k2" unfolding Bit_def apply (cases v1) @@ -562,53 +562,53 @@ lemma less_eq_Pls_Pls: - "Numeral.Pls \ Numeral.Pls \ True" by rule+ + "Int.Pls \ Int.Pls \ True" by rule+ lemma less_eq_Pls_Min: - "Numeral.Pls \ Numeral.Min \ False" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Pls \ Int.Min \ False" + unfolding Pls_def Int.Min_def by presburger lemma less_eq_Pls_Bit: - "Numeral.Pls \ Numeral.Bit k v \ Numeral.Pls \ k" + "Int.Pls \ Int.Bit k v \ Int.Pls \ k" unfolding Pls_def Bit_def by (cases v) auto lemma less_eq_Min_Pls: - "Numeral.Min \ Numeral.Pls \ True" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Min \ Int.Pls \ True" + unfolding Pls_def Int.Min_def by presburger lemma less_eq_Min_Min: - "Numeral.Min \ Numeral.Min \ True" by rule+ + "Int.Min \ Int.Min \ True" by rule+ lemma less_eq_Min_Bit0: - "Numeral.Min \ Numeral.Bit k bit.B0 \ Numeral.Min < k" - unfolding Numeral.Min_def Bit_def by auto + "Int.Min \ Int.Bit k bit.B0 \ Int.Min < k" + unfolding Int.Min_def Bit_def by auto lemma less_eq_Min_Bit1: - "Numeral.Min \ Numeral.Bit k bit.B1 \ Numeral.Min \ k" - unfolding Numeral.Min_def Bit_def by auto + "Int.Min \ Int.Bit k bit.B1 \ Int.Min \ k" + unfolding Int.Min_def Bit_def by auto lemma less_eq_Bit0_Pls: - "Numeral.Bit k bit.B0 \ Numeral.Pls \ k \ Numeral.Pls" + "Int.Bit k bit.B0 \ Int.Pls \ k \ Int.Pls" unfolding Pls_def Bit_def by simp lemma less_eq_Bit1_Pls: - "Numeral.Bit k bit.B1 \ Numeral.Pls \ k < Numeral.Pls" + "Int.Bit k bit.B1 \ Int.Pls \ k < Int.Pls" unfolding Pls_def Bit_def by auto lemma less_eq_Bit_Min: - "Numeral.Bit k v \ Numeral.Min \ k \ Numeral.Min" - unfolding Numeral.Min_def Bit_def by (cases v) auto + "Int.Bit k v \ Int.Min \ k \ Int.Min" + unfolding Int.Min_def Bit_def by (cases v) auto lemma less_eq_Bit0_Bit: - "Numeral.Bit k1 bit.B0 \ Numeral.Bit k2 v \ k1 \ k2" + "Int.Bit k1 bit.B0 \ Int.Bit k2 v \ k1 \ k2" unfolding Bit_def bit.cases by (cases v) auto lemma less_eq_Bit_Bit1: - "Numeral.Bit k1 v \ Numeral.Bit k2 bit.B1 \ k1 \ k2" + "Int.Bit k1 v \ Int.Bit k2 bit.B1 \ k1 \ k2" unfolding Bit_def bit.cases by (cases v) auto lemma less_eq_Bit1_Bit0: - "Numeral.Bit k1 bit.B1 \ Numeral.Bit k2 bit.B0 \ k1 < k2" + "Int.Bit k1 bit.B1 \ Int.Bit k2 bit.B0 \ k1 < k2" unfolding Bit_def by (auto split: bit.split) lemma less_eq_number_of: @@ -617,53 +617,53 @@ lemma less_Pls_Pls: - "Numeral.Pls < Numeral.Pls \ False" by simp + "Int.Pls < Int.Pls \ False" by simp lemma less_Pls_Min: - "Numeral.Pls < Numeral.Min \ False" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Pls < Int.Min \ False" + unfolding Pls_def Int.Min_def by presburger lemma less_Pls_Bit0: - "Numeral.Pls < Numeral.Bit k bit.B0 \ Numeral.Pls < k" + "Int.Pls < Int.Bit k bit.B0 \ Int.Pls < k" unfolding Pls_def Bit_def by auto lemma less_Pls_Bit1: - "Numeral.Pls < Numeral.Bit k bit.B1 \ Numeral.Pls \ k" + "Int.Pls < Int.Bit k bit.B1 \ Int.Pls \ k" unfolding Pls_def Bit_def by auto lemma less_Min_Pls: - "Numeral.Min < Numeral.Pls \ True" - unfolding Pls_def Numeral.Min_def by presburger + "Int.Min < Int.Pls \ True" + unfolding Pls_def Int.Min_def by presburger lemma less_Min_Min: - "Numeral.Min < Numeral.Min \ False" by simp + "Int.Min < Int.Min \ False" by simp lemma less_Min_Bit: - "Numeral.Min < Numeral.Bit k v \ Numeral.Min < k" - unfolding Numeral.Min_def Bit_def by (auto split: bit.split) + "Int.Min < Int.Bit k v \ Int.Min < k" + unfolding Int.Min_def Bit_def by (auto split: bit.split) lemma less_Bit_Pls: - "Numeral.Bit k v < Numeral.Pls \ k < Numeral.Pls" + "Int.Bit k v < Int.Pls \ k < Int.Pls" unfolding Pls_def Bit_def by (auto split: bit.split) lemma less_Bit0_Min: - "Numeral.Bit k bit.B0 < Numeral.Min \ k \ Numeral.Min" - unfolding Numeral.Min_def Bit_def by auto + "Int.Bit k bit.B0 < Int.Min \ k \ Int.Min" + unfolding Int.Min_def Bit_def by auto lemma less_Bit1_Min: - "Numeral.Bit k bit.B1 < Numeral.Min \ k < Numeral.Min" - unfolding Numeral.Min_def Bit_def by auto + "Int.Bit k bit.B1 < Int.Min \ k < Int.Min" + unfolding Int.Min_def Bit_def by auto lemma less_Bit_Bit0: - "Numeral.Bit k1 v < Numeral.Bit k2 bit.B0 \ k1 < k2" + "Int.Bit k1 v < Int.Bit k2 bit.B0 \ k1 < k2" unfolding Bit_def by (auto split: bit.split) lemma less_Bit1_Bit: - "Numeral.Bit k1 bit.B1 < Numeral.Bit k2 v \ k1 < k2" + "Int.Bit k1 bit.B1 < Int.Bit k2 v \ k1 < k2" unfolding Bit_def by (auto split: bit.split) lemma less_Bit0_Bit1: - "Numeral.Bit k1 bit.B0 < Numeral.Bit k2 bit.B1 \ k1 \ k2" + "Int.Bit k1 bit.B0 < Int.Bit k2 bit.B1 \ k1 \ k2" unfolding Bit_def bit.cases by arith lemma less_number_of: