# Theory K_R

theory K_R
imports RMD_Specification
begin
spark_open ‹rmd/k_r›
spark_vc function_k_r_6
using assms by (simp add: K'_def)
spark_vc function_k_r_7
proof-
from H1 have "16 <= nat j" by simp
moreover from H2 have "nat j <= 31" by simp
ultimately show ?thesis by (simp add: K'_def)
qed
spark_vc function_k_r_8
proof -
from H1 have "32 <= nat j" by simp
moreover from H2 have "nat j <= 47" by simp
ultimately show ?thesis by (simp add: K'_def)
qed
spark_vc function_k_r_9
proof -
from H1 have "48 <= nat j" by simp
moreover from H2 have "nat j <= 63" by simp
ultimately show ?thesis by (simp add: K'_def)
qed
spark_vc function_k_r_10
proof -
from H6 have "64 <= nat j" by simp
moreover from H2 have "nat j <= 79" by simp
ultimately show ?thesis by (simp add: K'_def)
qed
spark_end
end