"\<lbrakk>\<lbrace>P'\<rbrace> f \<lbrace>Q\<rbrace>, -; \<lbrace>P\<rbrace> f \<lbrace>Q'\<rbrace>, \<lbrace>E\<rbrace>\<rbrakk> \<Longrightarrow> \<lbrace>P and P'\<rbrace> f \<lbrace>\<lambda>r s. Q r s \<and> Q' r s\<rbrace>, \<lbrace>E\<rbrace>"
by (fastforce simp: validE_def validE_R_def valid_def split: sum.splits)