--- a/src/HOL/Lex/RegExp2NAe.ML Fri Jul 03 10:36:47 1998 +0200
+++ b/src/HOL/Lex/RegExp2NAe.ML Fri Jul 03 10:37:04 1998 +0200
@@ -31,23 +31,20 @@
qed "in_step_atom_Some";
Addsimps [in_step_atom_Some];
-Goal
- "([False],[False]) : steps (atom a) w = (w = [])";
+Goal "([False],[False]) : steps (atom a) w = (w = [])";
by (induct_tac "w" 1);
by(Simp_tac 1);
by(asm_simp_tac (simpset() addsimps [comp_def]) 1);
qed "False_False_in_steps_atom";
-Goal
- "(start (atom a), [False]) : steps (atom a) w = (w = [a])";
+Goal "(start (atom a), [False]) : steps (atom a) w = (w = [a])";
by (induct_tac "w" 1);
by(asm_simp_tac (simpset() addsimps [start_atom,rtrancl_empty]) 1);
by(asm_full_simp_tac (simpset()
addsimps [False_False_in_steps_atom,comp_def,start_atom]) 1);
qed "start_fin_in_steps_atom";
-Goal
- "accepts (atom a) w = (w = [a])";
+Goal "accepts (atom a) w = (w = [a])";
by(simp_tac(simpset() addsimps
[accepts_def,start_fin_in_steps_atom,fin_atom]) 1);
qed "accepts_atom";
@@ -90,7 +87,7 @@
(***** True/False ueber epsclosure anheben *****)
Goal
- "!!d. (tp,tq) : (eps(union L R))^* ==> \
+ "(tp,tq) : (eps(union L R))^* ==> \
\ !p. tp = True#p --> (? q. (p,q) : (eps L)^* & tq = True#q)";
be rtrancl_induct 1;
by(Blast_tac 1);
@@ -100,7 +97,7 @@
val lemma1a = result();
Goal
- "!!d. (tp,tq) : (eps(union L R))^* ==> \
+ "(tp,tq) : (eps(union L R))^* ==> \
\ !p. tp = False#p --> (? q. (p,q) : (eps R)^* & tq = False#q)";
be rtrancl_induct 1;
by(Blast_tac 1);
@@ -110,14 +107,14 @@
val lemma1b = result();
Goal
- "!!p. (p,q) : (eps L)^* ==> (True#p, True#q) : (eps(union L R))^*";
+ "(p,q) : (eps L)^* ==> (True#p, True#q) : (eps(union L R))^*";
be rtrancl_induct 1;
by(Blast_tac 1);
by(blast_tac (claset() addIs [rtrancl_into_rtrancl]) 1);
val lemma2a = result();
Goal
- "!!p. (p,q) : (eps R)^* ==> (False#p, False#q) : (eps(union L R))^*";
+ "(p,q) : (eps R)^* ==> (False#p, False#q) : (eps(union L R))^*";
be rtrancl_induct 1;
by(Blast_tac 1);
by(blast_tac (claset() addIs [rtrancl_into_rtrancl]) 1);
@@ -291,7 +288,7 @@
(** False in epsclosure **)
Goal
- "!!d. (tp,tq) : (eps(conc L R))^* ==> \
+ "(tp,tq) : (eps(conc L R))^* ==> \
\ !p. tp = False#p --> (? q. (p,q) : (eps R)^* & tq = False#q)";
by(etac rtrancl_induct 1);
by(Blast_tac 1);
@@ -299,7 +296,7 @@
qed "lemma1b";
Goal
- "!!p. (p,q) : (eps R)^* ==> (False#p, False#q) : (eps(conc L R))^*";
+ "(p,q) : (eps R)^* ==> (False#p, False#q) : (eps(conc L R))^*";
by(etac rtrancl_induct 1);
by(Blast_tac 1);
by(blast_tac (claset() addIs [rtrancl_into_rtrancl]) 1);
@@ -329,14 +326,14 @@
(** True in epsclosure **)
Goal
- "!!L R. (p,q): (eps L)^* ==> (True#p,True#q) : (eps(conc L R))^*";
+ "(p,q): (eps L)^* ==> (True#p,True#q) : (eps(conc L R))^*";
be rtrancl_induct 1;
by(Blast_tac 1);
by(blast_tac (claset() addIs [rtrancl_into_rtrancl]) 1);
qed "True_True_eps_concI";
Goal
- "!!L R. !p. (p,q) : steps L w --> (True#p,True#q) : steps (conc L R) w";
+ "!p. (p,q) : steps L w --> (True#p,True#q) : steps (conc L R) w";
by(induct_tac "w" 1);
by (simp_tac (simpset() addsimps [True_True_eps_concI]) 1);
by (Simp_tac 1);
@@ -344,7 +341,7 @@
qed_spec_mp "True_True_steps_concI";
Goal
- "!!d. (tp,tq) : (eps(conc L R))^* ==> \
+ "(tp,tq) : (eps(conc L R))^* ==> \
\ !p. tp = True#p --> \
\ (? q. tq = True#q & (p,q) : (eps L)^*) | \
\ (? q r. tq = False#q & (p,r):(eps L)^* & fin L r & (start R,q) : (eps R)^*)";
@@ -354,7 +351,7 @@
val lemma1a = result();
Goal
- "!!p. (p, q) : (eps L)^* ==> (True#p, True#q) : (eps(conc L R))^*";
+ "(p, q) : (eps L)^* ==> (True#p, True#q) : (eps(conc L R))^*";
by(etac rtrancl_induct 1);
by(Blast_tac 1);
by(blast_tac (claset() addIs [rtrancl_into_rtrancl]) 1);
@@ -367,7 +364,7 @@
val lemma = result();
Goal
- "!!L R. (p,q) : (eps R)^* ==> (False#p, False#q) : (eps(conc L R))^*";
+ "(p,q) : (eps R)^* ==> (False#p, False#q) : (eps(conc L R))^*";
by(etac rtrancl_induct 1);
by(Blast_tac 1);
by (dtac lemma 1);
@@ -477,7 +474,7 @@
qed_spec_mp "True_True_step_starI";
Goal
- "!!A. (p,r) : (eps A)^* ==> (True#p, True#r) : (eps(star A))^*";
+ "(p,r) : (eps A)^* ==> (True#p, True#r) : (eps(star A))^*";
be rtrancl_induct 1;
by(Blast_tac 1);
by(blast_tac (claset() addIs [True_True_step_starI,rtrancl_into_rtrancl]) 1);
@@ -489,7 +486,7 @@
qed_spec_mp "True_start_eps_starI";
Goal
- "!!dummy. (tp,s) : (eps(star A))^* ==> (! p. tp = True#p --> \
+ "(tp,s) : (eps(star A))^* ==> (! p. tp = True#p --> \
\ (? r. ((p,r) : (eps A)^* | \
\ (? q. (p,q) : (eps A)^* & fin A q & (start A,r) : (eps A)^*)) & \
\ s = True#r))";