src/HOL/Parity.thy
changeset 47225 650318981557
parent 47224 773fe2754b8c
child 54227 63b441f49645
equal deleted inserted replaced
47224:773fe2754b8c 47225:650318981557
   356 lemma lemma_even_mod_4_div_2: "n mod 4 = (1::nat) ==> even ((n - 1) div 2)"
   356 lemma lemma_even_mod_4_div_2: "n mod 4 = (1::nat) ==> even ((n - 1) div 2)"
   357   by presburger
   357   by presburger
   358 
   358 
   359 text {* Simplify, when the exponent is a numeral *}
   359 text {* Simplify, when the exponent is a numeral *}
   360 
   360 
   361 lemma power_0_left_numeral [simp]:
       
   362   "0 ^ numeral w = (0::'a::{power,semiring_0})"
       
   363 by (simp add: power_0_left)
       
   364 
       
   365 lemmas zero_le_power_eq_numeral [simp] =
   361 lemmas zero_le_power_eq_numeral [simp] =
   366     zero_le_power_eq [of _ "numeral w"] for w
   362     zero_le_power_eq [of _ "numeral w"] for w
   367 
   363 
   368 lemmas zero_less_power_eq_numeral [simp] =
   364 lemmas zero_less_power_eq_numeral [simp] =
   369     zero_less_power_eq [of _ "numeral w"] for w
   365     zero_less_power_eq [of _ "numeral w"] for w