equal
deleted
inserted
replaced
1490 qed |
1490 qed |
1491 |
1491 |
1492 lemma card_Un_disjoint: "finite A \<Longrightarrow> finite B \<Longrightarrow> A \<inter> B = {} \<Longrightarrow> card (A \<union> B) = card A + card B" |
1492 lemma card_Un_disjoint: "finite A \<Longrightarrow> finite B \<Longrightarrow> A \<inter> B = {} \<Longrightarrow> card (A \<union> B) = card A + card B" |
1493 using card_Un_Int [of A B] by simp |
1493 using card_Un_Int [of A B] by simp |
1494 |
1494 |
|
1495 lemma card_Un_disjnt: "\<lbrakk>finite A; finite B; disjnt A B\<rbrakk> \<Longrightarrow> card (A \<union> B) = card A + card B" |
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1496 by (simp add: card_Un_disjoint disjnt_def) |
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1497 |
1495 lemma card_Un_le: "card (A \<union> B) \<le> card A + card B" |
1498 lemma card_Un_le: "card (A \<union> B) \<le> card A + card B" |
1496 proof (cases "finite A \<and> finite B") |
1499 proof (cases "finite A \<and> finite B") |
1497 case True |
1500 case True |
1498 then show ?thesis |
1501 then show ?thesis |
1499 using le_iff_add card_Un_Int [of A B] by auto |
1502 using le_iff_add card_Un_Int [of A B] by auto |