author nipkow Sun Nov 28 15:21:02 2010 +0100 (2010-11-28) changeset 40787 d122dce6562d parent 40781 ba5be5c3d477 parent 40786 0a54cfc9add3 child 40788 61ebeb050db1 child 40796 aeeb3e61e3af
merged
```     1.1 --- a/src/HOL/Algebra/FiniteProduct.thy	Sun Nov 28 14:01:20 2010 +0100
1.2 +++ b/src/HOL/Algebra/FiniteProduct.thy	Sun Nov 28 15:21:02 2010 +0100
1.3 @@ -130,7 +130,7 @@
1.4     apply (rule Suc_le_mono [THEN subst])
1.6    apply (rule_tac A1 = "Aa - {xb}" in finite_imp_foldSetD [THEN exE])
1.7 -     apply (blast intro: foldSetD_imp_finite finite_Diff)
1.8 +     apply (blast intro: foldSetD_imp_finite)
1.9      apply best
1.10     apply assumption
1.11    apply (frule (1) Diff1_foldSetD)
```
```     2.1 --- a/src/HOL/Big_Operators.thy	Sun Nov 28 14:01:20 2010 +0100
2.2 +++ b/src/HOL/Big_Operators.thy	Sun Nov 28 15:21:02 2010 +0100
2.3 @@ -707,7 +707,7 @@
2.4  proof -
2.5    have "A <+> B = Inl ` A \<union> Inr ` B" by auto
2.6    moreover from fin have "finite (Inl ` A :: ('a + 'b) set)" "finite (Inr ` B :: ('a + 'b) set)"
2.7 -    by(auto intro: finite_imageI)
2.8 +    by auto
2.9    moreover have "Inl ` A \<inter> Inr ` B = ({} :: ('a + 'b) set)" by auto
2.10    moreover have "inj_on (Inl :: 'a \<Rightarrow> 'a + 'b) A" "inj_on (Inr :: 'b \<Rightarrow> 'a + 'b) B" by(auto intro: inj_onI)
2.11    ultimately show ?thesis using fin by(simp add: setsum_Un_disjoint setsum_reindex)
```
```     3.1 --- a/src/HOL/Finite_Set.thy	Sun Nov 28 14:01:20 2010 +0100
3.2 +++ b/src/HOL/Finite_Set.thy	Sun Nov 28 15:21:02 2010 +0100
3.3 @@ -274,7 +274,7 @@
3.4    then show ?thesis by simp
3.5  qed
3.6
3.7 -lemma finite_Diff [simp]: "finite A ==> finite (A - B)"
3.8 +lemma finite_Diff [simp, intro]: "finite A ==> finite (A - B)"
3.9  by (rule Diff_subset [THEN finite_subset])
3.10
3.11  lemma finite_Diff2 [simp]:
3.12 @@ -303,7 +303,7 @@
3.13
3.14  text {* Image and Inverse Image over Finite Sets *}
3.15
3.16 -lemma finite_imageI[simp]: "finite F ==> finite (h ` F)"
3.17 +lemma finite_imageI[simp, intro]: "finite F ==> finite (h ` F)"
3.18    -- {* The image of a finite set is finite. *}
3.19    by (induct set: finite) simp_all
3.20
3.21 @@ -372,8 +372,9 @@
3.22
3.23  text {* The finite UNION of finite sets *}
3.24
3.25 -lemma finite_UN_I: "finite A ==> (!!a. a:A ==> finite (B a)) ==> finite (UN a:A. B a)"
3.26 -  by (induct set: finite) simp_all
3.27 +lemma finite_UN_I[intro]:
3.28 +  "finite A ==> (!!a. a:A ==> finite (B a)) ==> finite (UN a:A. B a)"
3.29 +by (induct set: finite) simp_all
3.30
3.31  text {*
3.32    Strengthen RHS to
3.33 @@ -385,7 +386,7 @@
3.34
3.35  lemma finite_UN [simp]:
3.36    "finite A ==> finite (UNION A B) = (ALL x:A. finite (B x))"
3.37 -by (blast intro: finite_UN_I finite_subset)
3.38 +by (blast intro: finite_subset)
3.39
3.40  lemma finite_Collect_bex[simp]: "finite A \<Longrightarrow>
3.41    finite{x. EX y:A. Q x y} = (ALL y:A. finite{x. Q x y})"
3.42 @@ -428,9 +429,9 @@
3.43
3.44  text {* Sigma of finite sets *}
3.45
3.46 -lemma finite_SigmaI [simp]:
3.47 +lemma finite_SigmaI [simp, intro]:
3.48      "finite A ==> (!!a. a:A ==> finite (B a)) ==> finite (SIGMA a:A. B a)"
3.49 -  by (unfold Sigma_def) (blast intro!: finite_UN_I)
3.50 +  by (unfold Sigma_def) blast
3.51
3.52  lemma finite_cartesian_product: "[| finite A; finite B |] ==>
3.53      finite (A <*> B)"
3.54 @@ -2266,7 +2267,7 @@
3.55  apply (induct set: finite)
3.57  apply (subst card_Un_disjoint, blast)
3.58 -  apply (blast intro: finite_imageI, blast)
3.59 +  apply (blast, blast)
3.60  apply (subgoal_tac "inj_on (insert x) (Pow F)")
3.61   apply (simp add: card_image Pow_insert)
3.62  apply (unfold inj_on_def)
```
```     4.1 --- a/src/HOL/IMPP/Hoare.thy	Sun Nov 28 14:01:20 2010 +0100
4.2 +++ b/src/HOL/IMPP/Hoare.thy	Sun Nov 28 15:21:02 2010 +0100
4.3 @@ -367,7 +367,7 @@
4.4  apply  (tactic {* ALLGOALS (clarsimp_tac @{clasimpset}) *})
4.5  apply  (subgoal_tac "G = mgt_call ` U")
4.6  prefer 2
4.7 -apply   (simp add: card_seteq finite_imageI)
4.9  apply  simp
4.10  apply  (erule prems(3-)) (*MGF_lemma1*)
4.11  apply (rule ballI)
```
```     5.1 --- a/src/HOL/Library/Infinite_Set.thy	Sun Nov 28 14:01:20 2010 +0100
5.2 +++ b/src/HOL/Library/Infinite_Set.thy	Sun Nov 28 15:21:02 2010 +0100
5.3 @@ -339,7 +339,7 @@
5.4    shows "\<exists>y \<in> f`A. infinite (f -` {y})"
5.5  proof (rule ccontr)
5.6    assume "\<not> ?thesis"
5.7 -  with img have "finite (UN y:f`A. f -` {y})" by (blast intro: finite_UN_I)
5.8 +  with img have "finite (UN y:f`A. f -` {y})" by blast
5.9    moreover have "A \<subseteq> (UN y:f`A. f -` {y})" by auto
5.10    moreover note dom
5.11    ultimately show False by (simp add: infinite_super)
```
```     6.1 --- a/src/HOL/List.thy	Sun Nov 28 14:01:20 2010 +0100
6.2 +++ b/src/HOL/List.thy	Sun Nov 28 15:21:02 2010 +0100
6.3 @@ -3625,7 +3625,7 @@
6.4    have "?S (Suc n) = (\<Union>x\<in>A. (\<lambda>xs. x#xs) ` ?S n)"
6.5      by (auto simp:length_Suc_conv)
6.6    then show ?case using `finite A`
6.7 -    by (auto intro: finite_imageI Suc) (* FIXME metis? *)
6.8 +    by (auto intro: Suc) (* FIXME metis? *)
6.9  qed
6.10
6.11  lemma finite_lists_length_le:
```
```     7.1 --- a/src/HOL/Multivariate_Analysis/Cartesian_Euclidean_Space.thy	Sun Nov 28 14:01:20 2010 +0100
7.2 +++ b/src/HOL/Multivariate_Analysis/Cartesian_Euclidean_Space.thy	Sun Nov 28 15:21:02 2010 +0100
7.3 @@ -1300,7 +1300,7 @@
7.4    shows "finite {abs((x::'a::abs ^'n)\$i) |i. i\<in> (UNIV :: 'n set)}"
7.5    and "{abs(x\$i) |i. i\<in> (UNIV :: 'n::finite set)} \<noteq> {}"
7.6    unfolding  infnorm_set_image_cart
7.7 -  by (auto intro: finite_imageI)
7.8 +  by auto
7.9
7.10  lemma component_le_infnorm_cart:
7.11    shows "\<bar>x\$i\<bar> \<le> infnorm (x::real^'n)"
```
```     8.1 --- a/src/HOL/Multivariate_Analysis/Euclidean_Space.thy	Sun Nov 28 14:01:20 2010 +0100
8.2 +++ b/src/HOL/Multivariate_Analysis/Euclidean_Space.thy	Sun Nov 28 15:21:02 2010 +0100
8.3 @@ -2929,7 +2929,7 @@
8.4        using sf B(3)
8.5        unfolding span_linear_image[OF lf] surj_def subset_eq image_iff
8.6        apply blast
8.7 -      using fB apply (blast intro: finite_imageI)
8.8 +      using fB apply blast
8.9        unfolding d[symmetric]
8.10        apply (rule card_image_le)
8.11        apply (rule fB)
8.12 @@ -3035,7 +3035,7 @@
8.13    shows "finite {abs((x::'a::euclidean_space)\$\$i) |i. i<DIM('a)}"
8.14    and "{abs(x\$\$i) |i. i<DIM('a::euclidean_space)} \<noteq> {}"
8.15    unfolding infnorm_set_image
8.16 -  by (auto intro: finite_imageI)
8.17 +  by auto
8.18
8.19  lemma infnorm_pos_le: "0 \<le> infnorm (x::'a::euclidean_space)"
8.20    unfolding infnorm_def
```
```     9.1 --- a/src/HOL/Old_Number_Theory/Euler.thy	Sun Nov 28 14:01:20 2010 +0100
9.2 +++ b/src/HOL/Old_Number_Theory/Euler.thy	Sun Nov 28 15:21:02 2010 +0100
9.3 @@ -94,7 +94,7 @@
9.4  subsection {* Properties of SetS *}
9.5
9.6  lemma SetS_finite: "2 < p ==> finite (SetS a p)"
9.7 -  by (auto simp add: SetS_def SRStar_finite [of p] finite_imageI)
9.8 +  by (auto simp add: SetS_def SRStar_finite [of p])
9.9
9.10  lemma SetS_elems_finite: "\<forall>X \<in> SetS a p. finite X"
9.11    by (auto simp add: SetS_def MultInvPair_def)
```
```    10.1 --- a/src/HOL/Old_Number_Theory/EulerFermat.thy	Sun Nov 28 14:01:20 2010 +0100
10.2 +++ b/src/HOL/Old_Number_Theory/EulerFermat.thy	Sun Nov 28 15:21:02 2010 +0100
10.3 @@ -257,8 +257,7 @@
10.4    apply (subst setprod_insert)
10.5      apply (rule_tac [2] Bnor_prod_power_aux)
10.6       apply (unfold inj_on_def)
10.7 -     apply (simp_all add: zmult_ac Bnor_fin finite_imageI
10.8 -       Bnor_mem_zle_swap)
10.9 +     apply (simp_all add: zmult_ac Bnor_fin Bnor_mem_zle_swap)
10.10    done
10.11
10.12
```
```    11.1 --- a/src/HOL/Old_Number_Theory/Finite2.thy	Sun Nov 28 14:01:20 2010 +0100
11.2 +++ b/src/HOL/Old_Number_Theory/Finite2.thy	Sun Nov 28 15:21:02 2010 +0100
11.3 @@ -55,7 +55,7 @@
11.4  subsection {* Cardinality of explicit finite sets *}
11.5
11.6  lemma finite_surjI: "[| B \<subseteq> f ` A; finite A |] ==> finite B"
11.7 -  by (simp add: finite_subset finite_imageI)
11.9
11.10  lemma bdd_nat_set_l_finite: "finite {y::nat . y < x}"
11.11    by (rule bounded_nat_set_is_finite) blast
```
```    12.1 --- a/src/HOL/Old_Number_Theory/Gauss.thy	Sun Nov 28 14:01:20 2010 +0100
12.2 +++ b/src/HOL/Old_Number_Theory/Gauss.thy	Sun Nov 28 15:21:02 2010 +0100
12.3 @@ -73,22 +73,22 @@
12.4    done
12.5
12.6  lemma finite_B: "finite (B)"
12.7 -  by (auto simp add: B_def finite_A finite_imageI)
12.8 +by (auto simp add: B_def finite_A)
12.9
12.10  lemma finite_C: "finite (C)"
12.11 -  by (auto simp add: C_def finite_B finite_imageI)
12.12 +by (auto simp add: C_def finite_B)
12.13
12.14  lemma finite_D: "finite (D)"
12.15 -  by (auto simp add: D_def finite_Int finite_C)
12.16 +by (auto simp add: D_def finite_Int finite_C)
12.17
12.18  lemma finite_E: "finite (E)"
12.19 -  by (auto simp add: E_def finite_Int finite_C)
12.20 +by (auto simp add: E_def finite_Int finite_C)
12.21
12.22  lemma finite_F: "finite (F)"
12.23 -  by (auto simp add: F_def finite_E finite_imageI)
12.24 +by (auto simp add: F_def finite_E)
12.25
12.26  lemma C_eq: "C = D \<union> E"
12.27 -  by (auto simp add: C_def D_def E_def)
12.28 +by (auto simp add: C_def D_def E_def)
12.29
12.30  lemma A_card_eq: "card A = nat ((p - 1) div 2)"
12.31    apply (auto simp add: A_def)
```
```    13.1 --- a/src/HOL/Probability/Lebesgue_Integration.thy	Sun Nov 28 14:01:20 2010 +0100
13.2 +++ b/src/HOL/Probability/Lebesgue_Integration.thy	Sun Nov 28 15:21:02 2010 +0100
13.3 @@ -511,7 +511,7 @@
13.4        (\<lambda>(x,y). f -` {x} \<inter> g -` {y} \<inter> space M) ` (f`space M \<times> g`space M)"
13.5        by auto
13.6      hence "finite (?p ` (A \<inter> space M))"
13.7 -      by (rule finite_subset) (auto intro: finite_SigmaI finite_imageI) }
13.8 +      by (rule finite_subset) auto }
13.9    note this[intro, simp]
13.10
13.11    { fix x assume "x \<in> space M"
```
```    14.1 --- a/src/HOL/ex/While_Combinator_Example.thy	Sun Nov 28 14:01:20 2010 +0100
14.2 +++ b/src/HOL/ex/While_Combinator_Example.thy	Sun Nov 28 15:21:02 2010 +0100
14.3 @@ -28,7 +28,7 @@
14.4   apply (fastsimp intro!: lfp_lowerbound)
14.5   apply (blast intro: wf_finite_psubset Int_lower2 [THEN [2] wf_subset])
14.6  apply (clarsimp simp add: finite_psubset_def order_less_le)
14.7 -apply (blast intro!: finite_Diff dest: monoD)
14.8 +apply (blast dest: monoD)
14.9  done
14.10
14.11
```