equal
deleted
inserted
replaced
196 |
196 |
197 instantiation %quote * :: (semigroup, semigroup) semigroup |
197 instantiation %quote * :: (semigroup, semigroup) semigroup |
198 begin |
198 begin |
199 |
199 |
200 definition %quote |
200 definition %quote |
201 mult_prod_def: "p1 \<otimes> p2 = (fst p1 \<otimes> fst p2, snd p1 \<otimes> snd p2)" |
201 mult_prod_def: "p\<^isub>1 \<otimes> p\<^isub>2 = (fst p\<^isub>1 \<otimes> fst p\<^isub>2, snd p\<^isub>1 \<otimes> snd p\<^isub>2)" |
202 |
202 |
203 instance %quote proof |
203 instance %quote proof |
204 fix p1 p2 p3 :: "\<alpha>\<Colon>semigroup \<times> \<beta>\<Colon>semigroup" |
204 fix p\<^isub>1 p\<^isub>2 p\<^isub>3 :: "\<alpha>\<Colon>semigroup \<times> \<beta>\<Colon>semigroup" |
205 show "p1 \<otimes> p2 \<otimes> p3 = p1 \<otimes> (p2 \<otimes> p3)" |
205 show "p\<^isub>1 \<otimes> p\<^isub>2 \<otimes> p\<^isub>3 = p\<^isub>1 \<otimes> (p\<^isub>2 \<otimes> p\<^isub>3)" |
206 unfolding mult_prod_def by (simp add: assoc) |
206 unfolding mult_prod_def by (simp add: assoc) |
207 qed |
207 qed |
208 |
208 |
209 end %quote |
209 end %quote |
210 |
210 |