diff -r 97f69d44f732 -r 97a8ff4e4ac9 src/HOL/Int.thy --- a/src/HOL/Int.thy Fri Oct 18 10:35:57 2013 +0200 +++ b/src/HOL/Int.thy Fri Oct 18 10:43:20 2013 +0200 @@ -450,7 +450,7 @@ It is proved here because attribute @{text arith_split} is not available in theory @{text Rings}. But is it really better than just rewriting with @{text abs_if}?*} -lemma abs_split [arith_split,no_atp]: +lemma abs_split [arith_split, no_atp]: "P(abs(a::'a::linordered_idom)) = ((0 \ a --> P a) & (a < 0 --> P(-a)))" by (force dest: order_less_le_trans simp add: abs_if linorder_not_less) @@ -1158,32 +1158,32 @@ text{*To Simplify Inequalities Where One Side is the Constant 1*} -lemma less_minus_iff_1 [simp,no_atp]: +lemma less_minus_iff_1 [simp]: fixes b::"'b::linordered_idom" shows "(1 < - b) = (b < -1)" by auto -lemma le_minus_iff_1 [simp,no_atp]: +lemma le_minus_iff_1 [simp]: fixes b::"'b::linordered_idom" shows "(1 \ - b) = (b \ -1)" by auto -lemma equation_minus_iff_1 [simp,no_atp]: +lemma equation_minus_iff_1 [simp]: fixes b::"'b::ring_1" shows "(1 = - b) = (b = -1)" by (subst equation_minus_iff, auto) -lemma minus_less_iff_1 [simp,no_atp]: +lemma minus_less_iff_1 [simp]: fixes a::"'b::linordered_idom" shows "(- a < 1) = (-1 < a)" by auto -lemma minus_le_iff_1 [simp,no_atp]: +lemma minus_le_iff_1 [simp]: fixes a::"'b::linordered_idom" shows "(- a \ 1) = (-1 \ a)" by auto -lemma minus_equation_iff_1 [simp,no_atp]: +lemma minus_equation_iff_1 [simp]: fixes a::"'b::ring_1" shows "(- a = 1) = (a = -1)" by (subst minus_equation_iff, auto)