equal
deleted
inserted
replaced
41 next |
41 next |
42 case (Un a t) |
42 case (Un a t) |
43 show "(a Un t) Un u : ?T" |
43 show "(a Un t) Un u : ?T" |
44 proof - |
44 proof - |
45 have "a Un (t Un u) : ?T" |
45 have "a Un (t Un u) : ?T" |
46 using `a : A` |
46 using `a : A` |
47 proof (rule tiling.Un) |
47 proof (rule tiling.Un) |
48 from `(a Un t) Int u = {}` have "t Int u = {}" by blast |
48 from `(a Un t) Int u = {}` have "t Int u = {}" by blast |
49 then show "t Un u: ?T" by (rule Un) |
49 then show "t Un u: ?T" by (rule Un) |
50 from `a <= - t` and `(a Un t) Int u = {}` |
50 from `a <= - t` and `(a Un t) Int u = {}` |
51 show "a <= - (t Un u)" by blast |
51 show "a <= - (t Un u)" by blast |
52 qed |
52 qed |
53 also have "a Un (t Un u) = (a Un t) Un u" |
53 also have "a Un (t Un u) = (a Un t) Un u" |
54 by (simp only: Un_assoc) |
54 by (simp only: Un_assoc) |
55 finally show ?thesis . |
55 finally show ?thesis . |
56 qed |
56 qed |
227 qed |
227 qed |
228 moreover have "... Un ?e t b = insert (i, j) (?e t b)" by simp |
228 moreover have "... Un ?e t b = insert (i, j) (?e t b)" by simp |
229 moreover have "card ... = Suc (card (?e t b))" |
229 moreover have "card ... = Suc (card (?e t b))" |
230 proof (rule card_insert_disjoint) |
230 proof (rule card_insert_disjoint) |
231 from `t \<in> tiling domino` have "finite t" |
231 from `t \<in> tiling domino` have "finite t" |
232 by (rule tiling_domino_finite) |
232 by (rule tiling_domino_finite) |
233 then show "finite (?e t b)" |
233 then show "finite (?e t b)" |
234 by (rule evnodd_finite) |
234 by (rule evnodd_finite) |
235 from e have "(i, j) : ?e a b" by simp |
235 from e have "(i, j) : ?e a b" by simp |
236 with at show "(i, j) ~: ?e t b" by (blast dest: evnoddD) |
236 with at show "(i, j) ~: ?e t b" by (blast dest: evnoddD) |
237 qed |
237 qed |