tuned proofs
authorhaftmann
Mon Feb 08 17:12:30 2010 +0100 (2010-02-08)
changeset 3504882ab78fff970
parent 35047 1b2bae06c796
child 35049 00f311c32444
tuned proofs
src/HOL/Old_Number_Theory/WilsonBij.thy
src/HOL/Old_Number_Theory/WilsonRuss.thy
src/HOL/Word/BinGeneral.thy
     1.1 --- a/src/HOL/Old_Number_Theory/WilsonBij.thy	Mon Feb 08 17:12:27 2010 +0100
     1.2 +++ b/src/HOL/Old_Number_Theory/WilsonBij.thy	Mon Feb 08 17:12:30 2010 +0100
     1.3 @@ -74,9 +74,9 @@
     1.4  lemma aux: "[a * (p - 1) = 1] (mod p) = [a = p - 1] (mod p)"
     1.5    -- {* same as @{text WilsonRuss} *}
     1.6    apply (unfold zcong_def)
     1.7 -  apply (simp add: OrderedGroup.diff_diff_eq diff_diff_eq2 zdiff_zmult_distrib2)
     1.8 +  apply (simp add: diff_diff_eq diff_diff_eq2 zdiff_zmult_distrib2)
     1.9    apply (rule_tac s = "p dvd -((a + 1) + (p * -a))" in trans)
    1.10 -   apply (simp add: mult_commute)
    1.11 +   apply (simp add: algebra_simps)
    1.12    apply (subst dvd_minus_iff)
    1.13    apply (subst zdvd_reduce)
    1.14    apply (rule_tac s = "p dvd (a + 1) + (p * -1)" in trans)
     2.1 --- a/src/HOL/Old_Number_Theory/WilsonRuss.thy	Mon Feb 08 17:12:27 2010 +0100
     2.2 +++ b/src/HOL/Old_Number_Theory/WilsonRuss.thy	Mon Feb 08 17:12:30 2010 +0100
     2.3 @@ -82,9 +82,9 @@
     2.4  lemma inv_not_p_minus_1_aux:
     2.5      "[a * (p - 1) = 1] (mod p) = [a = p - 1] (mod p)"
     2.6    apply (unfold zcong_def)
     2.7 -  apply (simp add: OrderedGroup.diff_diff_eq diff_diff_eq2 zdiff_zmult_distrib2)
     2.8 +  apply (simp add: diff_diff_eq diff_diff_eq2 zdiff_zmult_distrib2)
     2.9    apply (rule_tac s = "p dvd -((a + 1) + (p * -a))" in trans)
    2.10 -   apply (simp add: mult_commute)
    2.11 +   apply (simp add: algebra_simps)
    2.12    apply (subst dvd_minus_iff)
    2.13    apply (subst zdvd_reduce)
    2.14    apply (rule_tac s = "p dvd (a + 1) + (p * -1)" in trans)
     3.1 --- a/src/HOL/Word/BinGeneral.thy	Mon Feb 08 17:12:27 2010 +0100
     3.2 +++ b/src/HOL/Word/BinGeneral.thy	Mon Feb 08 17:12:30 2010 +0100
     3.3 @@ -742,7 +742,7 @@
     3.4  
     3.5  lemma sb_inc_lem':
     3.6    "(a::int) < - (2^k) \<Longrightarrow> a + 2^k + 2^(Suc k) <= (a + 2^k) mod 2^(Suc k)"
     3.7 -  by (rule iffD1 [OF less_diff_eq, THEN sb_inc_lem, simplified OrderedGroup.diff_0])
     3.8 +  by (rule sb_inc_lem) simp
     3.9  
    3.10  lemma sbintrunc_inc:
    3.11    "x < - (2^n) ==> x + 2^(Suc n) <= sbintrunc n x"