60 lemma alpha_bp_eq: "alpha_bp = (op =)" |
60 lemma alpha_bp_eq: "alpha_bp = (op =)" |
61 apply (rule ext)+ |
61 apply (rule ext)+ |
62 apply (rule alpha_bp_eq_eq) |
62 apply (rule alpha_bp_eq_eq) |
63 done |
63 done |
64 |
64 |
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65 ML {* |
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66 fun build_eqvts funs perms simps induct ctxt = |
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67 let |
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68 val pi = Free ("pi", @{typ perm}); |
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69 val types = map (domain_type o fastype_of) funs; |
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70 val fv_indnames = Datatype_Prop.make_tnames (map body_type types); |
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71 val args = map Free (fv_indnames ~~ types); |
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72 val perm_at = Const (@{const_name permute}, @{typ "perm \<Rightarrow> atom set \<Rightarrow> atom set"}) |
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73 fun eqvtc (fv, (arg, perm)) = |
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74 HOLogic.mk_eq ((perm_at $ pi $ (fv $ arg)), (fv $ (perm $ pi $ arg))) |
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75 val gl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map eqvtc (funs ~~ (args ~~ perms)))) |
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76 fun tac _ = (indtac induct fv_indnames THEN_ALL_NEW |
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77 (asm_full_simp_tac (HOL_ss addsimps |
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78 (@{thm atom_eqvt} :: (Nominal_ThmDecls.get_eqvts_thms ctxt) @ simps)))) 1 |
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79 in |
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80 Goal.prove ctxt ("pi" :: fv_indnames) [] gl tac |
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81 end |
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82 *} |
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83 |
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84 ML {* |
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85 build_eqvts [@{term bv1}] [@{term "permute :: perm \<Rightarrow> bp \<Rightarrow> bp"}] (@{thms bv1.simps permute_rtrm1_permute_bp.simps}) @{thm rtrm1_bp.inducts(2)} @{context} |
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86 *} |
65 lemma bv1_eqvt[eqvt]: |
87 lemma bv1_eqvt[eqvt]: |
66 shows "(pi \<bullet> bv1 x) = bv1 (pi \<bullet> x)" |
88 shows "(pi \<bullet> bv1 x) = bv1 (pi \<bullet> x)" |
67 apply (induct x) |
89 apply (induct x) |
68 apply (simp_all add: eqvts atom_eqvt) |
90 apply (simp_all add: eqvts atom_eqvt) |
69 done |
91 done |
70 |
92 |
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93 ML {* |
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94 build_eqvts [@{term fv_rtrm1}, @{term fv_bp}] [@{term "permute :: perm \<Rightarrow> rtrm1 \<Rightarrow> rtrm1"},@{term "permute :: perm \<Rightarrow> bp \<Rightarrow> bp"}] (@{thms fv_rtrm1_fv_bp.simps permute_rtrm1_permute_bp.simps}) @{thm rtrm1_bp.induct} @{context} |
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95 *} |
71 lemma fv_rtrm1_eqvt[eqvt]: |
96 lemma fv_rtrm1_eqvt[eqvt]: |
72 "(pi\<bullet>fv_rtrm1 t) = fv_rtrm1 (pi\<bullet>t)" |
97 "(pi\<bullet>fv_rtrm1 t) = fv_rtrm1 (pi\<bullet>t)" |
73 "(pi\<bullet>fv_bp b) = fv_bp (pi\<bullet>b)" |
98 "(pi\<bullet>fv_bp b) = fv_bp (pi\<bullet>b)" |
74 apply (induct t and b) |
99 apply (induct t and b) |
75 apply (simp_all add: eqvts atom_eqvt) |
100 apply (simp_all add: eqvts atom_eqvt) |