equal
deleted
inserted
replaced
185 |
185 |
186 subclass factorial_semiring |
186 subclass factorial_semiring |
187 proof - |
187 proof - |
188 show "class.factorial_semiring divide plus minus zero times one |
188 show "class.factorial_semiring divide plus minus zero times one |
189 unit_factor normalize" |
189 unit_factor normalize" |
190 proof (standard, rule factorial_semiring_altI_aux) -- \<open>FIXME rule\<close> |
190 proof (standard, rule factorial_semiring_altI_aux) \<comment> \<open>FIXME rule\<close> |
191 fix x assume "x \<noteq> 0" |
191 fix x assume "x \<noteq> 0" |
192 thus "finite {p. p dvd x \<and> normalize p = p}" |
192 thus "finite {p. p dvd x \<and> normalize p = p}" |
193 proof (induction "euclidean_size x" arbitrary: x rule: less_induct) |
193 proof (induction "euclidean_size x" arbitrary: x rule: less_induct) |
194 case (less x) |
194 case (less x) |
195 show ?case |
195 show ?case |