src/HOL/Fields.thy
changeset 53374 a14d2a854c02
parent 53215 5e47c31c6f7c
child 54147 97a8ff4e4ac9
equal deleted inserted replaced
53373:3ca9e79ac926 53374:a14d2a854c02
   917     show ?thesis by simp
   917     show ?thesis by simp
   918 next
   918 next
   919   assume notless: "~ (0 < x)"
   919   assume notless: "~ (0 < x)"
   920   have "~ (1 < inverse x)"
   920   have "~ (1 < inverse x)"
   921   proof
   921   proof
   922     assume "1 < inverse x"
   922     assume *: "1 < inverse x"
   923     also with notless have "... \<le> 0" by simp
   923     also from notless and * have "... \<le> 0" by simp
   924     also have "... < 1" by (rule zero_less_one) 
   924     also have "... < 1" by (rule zero_less_one) 
   925     finally show False by auto
   925     finally show False by auto
   926   qed
   926   qed
   927   with notless show ?thesis by simp
   927   with notless show ?thesis by simp
   928 qed
   928 qed