src/HOL/Power.thy
changeset 54489 03ff4d1e6784
parent 54249 ce00f2fef556
child 55096 916b2ac758f4
equal deleted inserted replaced
54488:b60f1fab408c 54489:03ff4d1e6784
   206     power_one_right mult_minus_left mult_minus_right minus_minus)
   206     power_one_right mult_minus_left mult_minus_right minus_minus)
   207 
   207 
   208 lemma power_minus_Bit1:
   208 lemma power_minus_Bit1:
   209   "(- x) ^ numeral (Num.Bit1 k) = - (x ^ numeral (Num.Bit1 k))"
   209   "(- x) ^ numeral (Num.Bit1 k) = - (x ^ numeral (Num.Bit1 k))"
   210   by (simp only: eval_nat_numeral(3) power_Suc power_minus_Bit0 mult_minus_left)
   210   by (simp only: eval_nat_numeral(3) power_Suc power_minus_Bit0 mult_minus_left)
   211 
       
   212 lemma power_neg_numeral_Bit0 [simp]:
       
   213   "neg_numeral k ^ numeral (Num.Bit0 l) = numeral (Num.pow k (Num.Bit0 l))"
       
   214   by (simp only: neg_numeral_def power_minus_Bit0 power_numeral)
       
   215 
       
   216 lemma power_neg_numeral_Bit1 [simp]:
       
   217   "neg_numeral k ^ numeral (Num.Bit1 l) = neg_numeral (Num.pow k (Num.Bit1 l))"
       
   218   by (simp only: neg_numeral_def power_minus_Bit1 power_numeral pow.simps)
       
   219 
   211 
   220 lemma power2_minus [simp]:
   212 lemma power2_minus [simp]:
   221   "(- a)\<^sup>2 = a\<^sup>2"
   213   "(- a)\<^sup>2 = a\<^sup>2"
   222   by (rule power_minus_Bit0)
   214   by (rule power_minus_Bit0)
   223 
   215