1 theory Minimal

     2 imports "Nominal"

     3 begin

     4 

     5 atom_decl name

     6 

     7 nominal_datatype lam =

     8   Var "name"

     9 | App "lam" "lam" 

    10 | Lam "\<guillemotleft>name\<guillemotright>lam" ("Lam [_]._")

    11 

    12 lemma alpha_test:

    13   shows "Lam [x].Var x = Lam [y].Var y"

    14   by (simp add: lam.inject alpha swap_simps fresh_atm)

    15 

    16 thm lam.inject[no_vars]

    17 thm alpha[no_vars]

    18 thm swap_simps[no_vars]

    19 thm fresh_atm[no_vars]

    20 

    21 end