Subst/UTLemmas.ML
changeset 171 16c4ea954511
parent 124 ee29edc644e8
equal deleted inserted replaced
170:3a8d722fd3ff 171:16c4ea954511
    28 
    28 
    29 goal UTLemmas.thy  "t <: u & u <: v --> t <: v";
    29 goal UTLemmas.thy  "t <: u & u <: v --> t <: v";
    30 by (uterm_ind_tac "v" 1);
    30 by (uterm_ind_tac "v" 1);
    31 by (ALLGOALS (simp_tac utlemmas_ss));
    31 by (ALLGOALS (simp_tac utlemmas_ss));
    32 by (fast_tac HOL_cs 1);
    32 by (fast_tac HOL_cs 1);
    33 val occs_trans = conjI RS (result() RS mp);
    33 val occs_trans  = store_thm("occs_trans", conjI RS (result() RS mp));
    34 
    34 
    35 goal UTLemmas.thy   "~ t <: v --> ~ t <: u | ~ u <: v";
    35 goal UTLemmas.thy   "~ t <: v --> ~ t <: u | ~ u <: v";
    36 by (fast_tac (HOL_cs addIs [occs_trans]) 1);
    36 by (fast_tac (HOL_cs addIs [occs_trans]) 1);
    37 val contr_occs_trans = result() RS mp;
    37 val contr_occs_trans  = store_thm("contr_occs_trans", result() RS mp);
    38 
    38 
    39 goal UTLemmas.thy   "t <: Comb(t,u)";
    39 goal UTLemmas.thy   "t <: Comb(t,u)";
    40 by (simp_tac utlemmas_ss 1);
    40 by (simp_tac utlemmas_ss 1);
    41 val occs_Comb1 = result();
    41 qed "occs_Comb1";
    42 
    42 
    43 goal UTLemmas.thy  "u <: Comb(t,u)";
    43 goal UTLemmas.thy  "u <: Comb(t,u)";
    44 by (simp_tac utlemmas_ss 1);
    44 by (simp_tac utlemmas_ss 1);
    45 val occs_Comb2 = result();
    45 qed "occs_Comb2";
    46 
    46 
    47 goal HOL.thy  "(~(P|Q)) = (~P & ~Q)";
    47 goal HOL.thy  "(~(P|Q)) = (~P & ~Q)";
    48 by (fast_tac HOL_cs 1);
    48 by (fast_tac HOL_cs 1);
    49 val demorgan_disj = result();
    49 qed "demorgan_disj";
    50 
    50 
    51 goal UTLemmas.thy  "~ t <: t";
    51 goal UTLemmas.thy  "~ t <: t";
    52 by (uterm_ind_tac "t" 1);
    52 by (uterm_ind_tac "t" 1);
    53 by (ALLGOALS (simp_tac (utlemmas_ss addsimps [demorgan_disj])));
    53 by (ALLGOALS (simp_tac (utlemmas_ss addsimps [demorgan_disj])));
    54 by (REPEAT (resolve_tac [impI,conjI] 1 ORELSE
    54 by (REPEAT (resolve_tac [impI,conjI] 1 ORELSE
    55             (etac contrapos 1 THEN etac subst 1 THEN 
    55             (etac contrapos 1 THEN etac subst 1 THEN 
    56              resolve_tac [occs_Comb1,occs_Comb2] 1) ORELSE
    56              resolve_tac [occs_Comb1,occs_Comb2] 1) ORELSE
    57             (etac (contr_occs_trans RS disjE) 1 THEN assume_tac 2) ORELSE
    57             (etac (contr_occs_trans RS disjE) 1 THEN assume_tac 2) ORELSE
    58             eresolve_tac ([occs_Comb1,occs_Comb2] RLN(2,[notE])) 1));
    58             eresolve_tac ([occs_Comb1,occs_Comb2] RLN(2,[notE])) 1));
    59 val occs_irrefl = result();
    59 qed "occs_irrefl";
    60 
    60 
    61 goal UTLemmas.thy  "t <: u --> ~t=u";
    61 goal UTLemmas.thy  "t <: u --> ~t=u";
    62 by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1);
    62 by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1);
    63 val occs_irrefl2 = result() RS mp;
    63 val occs_irrefl2  = store_thm("occs_irrefl2", result() RS mp);
    64 
    64 
    65 
    65 
    66 (**** vars_of lemmas  ****)
    66 (**** vars_of lemmas  ****)
    67 
    67 
    68 goal UTLemmas.thy "(v : vars_of(Var(w))) = (w=v)";
    68 goal UTLemmas.thy "(v : vars_of(Var(w))) = (w=v)";
    69 by (simp_tac utlemmas_ss 1);
    69 by (simp_tac utlemmas_ss 1);
    70 by (fast_tac HOL_cs 1);
    70 by (fast_tac HOL_cs 1);
    71 val vars_var_iff = result();
    71 qed "vars_var_iff";
    72 
    72 
    73 goal UTLemmas.thy  "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)";
    73 goal UTLemmas.thy  "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)";
    74 by (uterm_ind_tac "t" 1);
    74 by (uterm_ind_tac "t" 1);
    75 by (ALLGOALS (simp_tac utlemmas_ss));
    75 by (ALLGOALS (simp_tac utlemmas_ss));
    76 by (fast_tac HOL_cs 1);
    76 by (fast_tac HOL_cs 1);
    77 val vars_iff_occseq = result();
    77 qed "vars_iff_occseq";