1 lemma exi: "\<exists>(pi :: perm). P pi \<Longrightarrow> (\<And>(p :: perm). P p \<Longrightarrow> Q (pi \<bullet> p)) \<Longrightarrow> \<exists>pi. Q pi"

     2 apply (erule exE)

     3 apply (rule_tac x="pi \<bullet> pia" in exI)

     4 by auto

     5 

     6 ML {*

     7 fun alpha_eqvt_tac induct simps ctxt =

     8   rtac induct THEN_ALL_NEW

     9   simp_tac (HOL_basic_ss addsimps simps) THEN_ALL_NEW split_conj_tac THEN_ALL_NEW

    10   REPEAT o etac @{thm exi[of _ _ "p"]} THEN' split_conj_tac THEN_ALL_NEW

    11   asm_full_simp_tac (HOL_ss addsimps (all_eqvts ctxt @ simps)) THEN_ALL_NEW

    12   asm_full_simp_tac (HOL_ss addsimps

    13     @{thms supp_eqvt[symmetric] inter_eqvt[symmetric] empty_eqvt alphas prod_rel.simps prod_fv.simps}) THEN_ALL_NEW

    14   (split_conj_tac THEN_ALL_NEW TRY o resolve_tac

    15     @{thms fresh_star_permute_iff[of "- p", THEN iffD1] permute_eq_iff[of "- p", THEN iffD1]})

    16   THEN_ALL_NEW

    17   asm_full_simp_tac (HOL_ss addsimps (@{thms split_conv permute_minus_cancel permute_plus permute_eqvt[symmetric]} @ all_eqvts ctxt @ simps))

    18 *}

    19 

    20 ML {*

    21 fun build_alpha_eqvt alpha names =

    22 let

    23   val pi = Free ("p", @{typ perm});

    24   val (tys, _) = strip_type (fastype_of alpha)

    25   val indnames = Name.variant_list names (Datatype_Prop.make_tnames (map body_type tys));

    26   val args = map Free (indnames ~~ tys);

    27   val perm_args = map (fn x => mk_perm pi x) args

    28 in

    29   (HOLogic.mk_imp (list_comb (alpha, args), list_comb (alpha, perm_args)), indnames @ names)

    30 end

    31 *}

    32 

    33 ML {*

    34 fun build_alpha_eqvts funs tac ctxt =

    35 let

    36   val (gls, names) = fold_map build_alpha_eqvt funs ["p"]

    37   val gl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj gls)

    38   val thm = Goal.prove ctxt names [] gl tac

    39 in

    40   map (fn x => mp OF [x]) (HOLogic.conj_elims thm)

    41 end

    42 *}

    43