--- a/HOL.ML Thu Dec 08 12:50:38 1994 +0100
+++ b/HOL.ML Fri Dec 09 13:39:05 1994 +0100
@@ -9,75 +9,16 @@
open HOL;
-signature HOL_LEMMAS =
- sig
- val allE : thm
- val all_dupE : thm
- val allI : thm
- val arg_cong : thm
- val fun_cong : thm
- val box_equals: thm
- val case_tac : string -> int -> tactic
- val ccontr : thm
- val classical : thm
- val cong : thm
- val conjunct1 : thm
- val conjunct2 : thm
- val conjE : thm
- val conjI : thm
- val contrapos : thm
- val disjCI : thm
- val disjE : thm
- val disjI1 : thm
- val disjI2 : thm
- val eqTrueI : thm
- val eqTrueE : thm
- val ex1E : thm
- val ex1I : thm
- val exCI : thm
- val exI : thm
- val exE : thm
- val excluded_middle : thm
- val excluded_middle_tac : string -> int -> tactic
- val False_neq_True : thm
- val FalseE : thm
- val iffCE : thm
- val iffD1 : thm
- val iffD2 : thm
- val iffE : thm
- val iffI : thm
- val impCE : thm
- val impE : thm
- val not_sym : thm
- val notE : thm
- val notI : thm
- val notnotD : thm
- val rev_mp : thm
- val select_equality : thm
- val selectI2 : thm
- val spec : thm
- val sstac : thm list -> int -> tactic
- val ssubst : thm
- val stac : thm -> int -> tactic
- val strip_tac : int -> tactic
- val sym : thm
- val trans : thm
- val TrueI : thm
- end;
-
-structure HOL_Lemmas : HOL_LEMMAS =
-
-struct
(** Equality **)
-val sym = prove_goal HOL.thy "s=t ==> t=s"
+qed_goal "sym" HOL.thy "s=t ==> t=s"
(fn prems => [cut_facts_tac prems 1, etac subst 1, rtac refl 1]);
(*calling "standard" reduces maxidx to 0*)
val ssubst = standard (sym RS subst);
-val trans = prove_goal HOL.thy "[| r=s; s=t |] ==> r=t"
+qed_goal "trans" HOL.thy "[| r=s; s=t |] ==> r=t"
(fn prems =>
[rtac subst 1, resolve_tac prems 1, resolve_tac prems 1]);
@@ -85,7 +26,7 @@
a = b
| |
c = d *)
-val box_equals = prove_goal HOL.thy
+qed_goal "box_equals" HOL.thy
"[| a=b; a=c; b=d |] ==> c=d"
(fn prems=>
[ (rtac trans 1),
@@ -96,58 +37,58 @@
(** Congruence rules for meta-application **)
(*similar to AP_THM in Gordon's HOL*)
-val fun_cong = prove_goal HOL.thy "(f::'a=>'b) = g ==> f(x)=g(x)"
+qed_goal "fun_cong" HOL.thy "(f::'a=>'b) = g ==> f(x)=g(x)"
(fn [prem] => [rtac (prem RS subst) 1, rtac refl 1]);
(*similar to AP_TERM in Gordon's HOL and FOL's subst_context*)
-val arg_cong = prove_goal HOL.thy "x=y ==> f(x)=f(y)"
+qed_goal "arg_cong" HOL.thy "x=y ==> f(x)=f(y)"
(fn [prem] => [rtac (prem RS subst) 1, rtac refl 1]);
-val cong = prove_goal HOL.thy
+qed_goal "cong" HOL.thy
"[| f = g; (x::'a) = y |] ==> f(x) = g(y)"
(fn [prem1,prem2] =>
[rtac (prem1 RS subst) 1, rtac (prem2 RS subst) 1, rtac refl 1]);
(** Equality of booleans -- iff **)
-val iffI = prove_goal HOL.thy
+qed_goal "iffI" HOL.thy
"[| P ==> Q; Q ==> P |] ==> P=Q"
(fn prems=> [ (REPEAT (ares_tac (prems@[impI, iff RS mp RS mp]) 1)) ]);
-val iffD2 = prove_goal HOL.thy "[| P=Q; Q |] ==> P"
+qed_goal "iffD2" HOL.thy "[| P=Q; Q |] ==> P"
(fn prems =>
[rtac ssubst 1, resolve_tac prems 1, resolve_tac prems 1]);
val iffD1 = sym RS iffD2;
-val iffE = prove_goal HOL.thy
+qed_goal "iffE" HOL.thy
"[| P=Q; [| P --> Q; Q --> P |] ==> R |] ==> R"
(fn [p1,p2] => [REPEAT(ares_tac([p1 RS iffD2, p1 RS iffD1, p2, impI])1)]);
(** True **)
-val TrueI = prove_goalw HOL.thy [True_def] "True"
+qed_goalw "TrueI" HOL.thy [True_def] "True"
(fn _ => [rtac refl 1]);
-val eqTrueI = prove_goal HOL.thy "P ==> P=True"
+qed_goal "eqTrueI " HOL.thy "P ==> P=True"
(fn prems => [REPEAT(resolve_tac ([iffI,TrueI]@prems) 1)]);
-val eqTrueE = prove_goal HOL.thy "P=True ==> P"
+qed_goal "eqTrueE" HOL.thy "P=True ==> P"
(fn prems => [REPEAT(resolve_tac (prems@[TrueI,iffD2]) 1)]);
(** Universal quantifier **)
-val allI = prove_goalw HOL.thy [All_def] "(!!x::'a. P(x)) ==> !x. P(x)"
+qed_goalw "allI" HOL.thy [All_def] "(!!x::'a. P(x)) ==> !x. P(x)"
(fn prems => [resolve_tac (prems RL [eqTrueI RS ext]) 1]);
-val spec = prove_goalw HOL.thy [All_def] "! x::'a.P(x) ==> P(x)"
+qed_goalw "spec" HOL.thy [All_def] "! x::'a.P(x) ==> P(x)"
(fn prems => [rtac eqTrueE 1, resolve_tac (prems RL [fun_cong]) 1]);
-val allE = prove_goal HOL.thy "[| !x.P(x); P(x) ==> R |] ==> R"
+qed_goal "allE" HOL.thy "[| !x.P(x); P(x) ==> R |] ==> R"
(fn major::prems=>
[ (REPEAT (resolve_tac (prems @ [major RS spec]) 1)) ]);
-val all_dupE = prove_goal HOL.thy
+qed_goal "all_dupE" HOL.thy
"[| ! x.P(x); [| P(x); ! x.P(x) |] ==> R |] ==> R"
(fn prems =>
[ (REPEAT (resolve_tac (prems @ (prems RL [spec])) 1)) ]);
@@ -156,31 +97,31 @@
(** False ** Depends upon spec; it is impossible to do propositional logic
before quantifiers! **)
-val FalseE = prove_goalw HOL.thy [False_def] "False ==> P"
+qed_goalw "FalseE" HOL.thy [False_def] "False ==> P"
(fn [major] => [rtac (major RS spec) 1]);
-val False_neq_True = prove_goal HOL.thy "False=True ==> P"
+qed_goal "False_neq_True" HOL.thy "False=True ==> P"
(fn [prem] => [rtac (prem RS eqTrueE RS FalseE) 1]);
(** Negation **)
-val notI = prove_goalw HOL.thy [not_def] "(P ==> False) ==> ~P"
+qed_goalw "notI" HOL.thy [not_def] "(P ==> False) ==> ~P"
(fn prems=> [rtac impI 1, eresolve_tac prems 1]);
-val notE = prove_goalw HOL.thy [not_def] "[| ~P; P |] ==> R"
+qed_goalw "notE" HOL.thy [not_def] "[| ~P; P |] ==> R"
(fn prems => [rtac (prems MRS mp RS FalseE) 1]);
(** Implication **)
-val impE = prove_goal HOL.thy "[| P-->Q; P; Q ==> R |] ==> R"
+qed_goal "impE" HOL.thy "[| P-->Q; P; Q ==> R |] ==> R"
(fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
(* Reduces Q to P-->Q, allowing substitution in P. *)
-val rev_mp = prove_goal HOL.thy "[| P; P --> Q |] ==> Q"
+qed_goal "rev_mp" HOL.thy "[| P; P --> Q |] ==> Q"
(fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
-val contrapos = prove_goal HOL.thy "[| ~Q; P==>Q |] ==> ~P"
+qed_goal "contrapos" HOL.thy "[| ~Q; P==>Q |] ==> ~P"
(fn [major,minor]=>
[ (rtac (major RS notE RS notI) 1),
(etac minor 1) ]);
@@ -191,49 +132,49 @@
(** Existential quantifier **)
-val exI = prove_goalw HOL.thy [Ex_def] "P(x) ==> ? x::'a.P(x)"
+qed_goalw "exI" HOL.thy [Ex_def] "P(x) ==> ? x::'a.P(x)"
(fn prems => [rtac selectI 1, resolve_tac prems 1]);
-val exE = prove_goalw HOL.thy [Ex_def]
+qed_goalw "exE" HOL.thy [Ex_def]
"[| ? x::'a.P(x); !!x. P(x) ==> Q |] ==> Q"
(fn prems => [REPEAT(resolve_tac prems 1)]);
(** Conjunction **)
-val conjI = prove_goalw HOL.thy [and_def] "[| P; Q |] ==> P&Q"
+qed_goalw "conjI" HOL.thy [and_def] "[| P; Q |] ==> P&Q"
(fn prems =>
[REPEAT (resolve_tac (prems@[allI,impI]) 1 ORELSE etac (mp RS mp) 1)]);
-val conjunct1 = prove_goalw HOL.thy [and_def] "[| P & Q |] ==> P"
+qed_goalw "conjunct1" HOL.thy [and_def] "[| P & Q |] ==> P"
(fn prems =>
[resolve_tac (prems RL [spec] RL [mp]) 1, REPEAT(ares_tac [impI] 1)]);
-val conjunct2 = prove_goalw HOL.thy [and_def] "[| P & Q |] ==> Q"
+qed_goalw "conjunct2" HOL.thy [and_def] "[| P & Q |] ==> Q"
(fn prems =>
[resolve_tac (prems RL [spec] RL [mp]) 1, REPEAT(ares_tac [impI] 1)]);
-val conjE = prove_goal HOL.thy "[| P&Q; [| P; Q |] ==> R |] ==> R"
+qed_goal "conjE" HOL.thy "[| P&Q; [| P; Q |] ==> R |] ==> R"
(fn prems =>
[cut_facts_tac prems 1, resolve_tac prems 1,
etac conjunct1 1, etac conjunct2 1]);
(** Disjunction *)
-val disjI1 = prove_goalw HOL.thy [or_def] "P ==> P|Q"
+qed_goalw "disjI1" HOL.thy [or_def] "P ==> P|Q"
(fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
-val disjI2 = prove_goalw HOL.thy [or_def] "Q ==> P|Q"
+qed_goalw "disjI2" HOL.thy [or_def] "Q ==> P|Q"
(fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
-val disjE = prove_goalw HOL.thy [or_def] "[| P | Q; P ==> R; Q ==> R |] ==> R"
+qed_goalw "disjE" HOL.thy [or_def] "[| P | Q; P ==> R; Q ==> R |] ==> R"
(fn [a1,a2,a3] =>
[rtac (mp RS mp) 1, rtac spec 1, rtac a1 1,
rtac (a2 RS impI) 1, assume_tac 1, rtac (a3 RS impI) 1, assume_tac 1]);
(** CCONTR -- classical logic **)
-val classical = prove_goalw HOL.thy [not_def] "(~P ==> P) ==> P"
+qed_goalw "classical" HOL.thy [not_def] "(~P ==> P) ==> P"
(fn [prem] =>
[rtac (True_or_False RS (disjE RS eqTrueE)) 1, assume_tac 1,
rtac (impI RS prem RS eqTrueI) 1,
@@ -242,19 +183,19 @@
val ccontr = FalseE RS classical;
(*Double negation law*)
-val notnotD = prove_goal HOL.thy "~~P ==> P"
+qed_goal "notnotD" HOL.thy "~~P ==> P"
(fn [major]=>
[ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]);
(** Unique existence **)
-val ex1I = prove_goalw HOL.thy [Ex1_def]
+qed_goalw "ex1I" HOL.thy [Ex1_def]
"[| P(a); !!x. P(x) ==> x=a |] ==> ?! x. P(x)"
(fn prems =>
[REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)]);
-val ex1E = prove_goalw HOL.thy [Ex1_def]
+qed_goalw "ex1E" HOL.thy [Ex1_def]
"[| ?! x.P(x); !!x. [| P(x); ! y. P(y) --> y=x |] ==> R |] ==> R"
(fn major::prems =>
[rtac (major RS exE) 1, REPEAT (etac conjE 1 ORELSE ares_tac prems 1)]);
@@ -263,13 +204,13 @@
(** Select: Hilbert's Epsilon-operator **)
(*Easier to apply than selectI: conclusion has only one occurrence of P*)
-val selectI2 = prove_goal HOL.thy
+qed_goal "selectI2" HOL.thy
"[| P(a); !!x. P(x) ==> Q(x) |] ==> Q(@x.P(x))"
(fn prems => [ resolve_tac prems 1,
rtac selectI 1,
resolve_tac prems 1 ]);
-val select_equality = prove_goal HOL.thy
+qed_goal "select_equality" HOL.thy
"[| P(a); !!x. P(x) ==> x=a |] ==> (@x.P(x)) = a"
(fn prems => [ rtac selectI2 1,
REPEAT (ares_tac prems 1) ]);
@@ -277,13 +218,13 @@
(** Classical intro rules for disjunction and existential quantifiers *)
-val disjCI = prove_goal HOL.thy "(~Q ==> P) ==> P|Q"
+qed_goal "disjCI" HOL.thy "(~Q ==> P) ==> P|Q"
(fn prems=>
[ (rtac classical 1),
(REPEAT (ares_tac (prems@[disjI1,notI]) 1)),
(REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);
-val excluded_middle = prove_goal HOL.thy "~P | P"
+qed_goal "excluded_middle" HOL.thy "~P | P"
(fn _ => [ (REPEAT (ares_tac [disjCI] 1)) ]);
(*For disjunctive case analysis*)
@@ -291,20 +232,20 @@
res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
(*Classical implies (-->) elimination. *)
-val impCE = prove_goal HOL.thy "[| P-->Q; ~P ==> R; Q ==> R |] ==> R"
+qed_goal "impCE" HOL.thy "[| P-->Q; ~P ==> R; Q ==> R |] ==> R"
(fn major::prems=>
[ rtac (excluded_middle RS disjE) 1,
REPEAT (DEPTH_SOLVE_1 (ares_tac (prems @ [major RS mp]) 1))]);
(*Classical <-> elimination. *)
-val iffCE = prove_goal HOL.thy
+qed_goal "iffCE" HOL.thy
"[| P=Q; [| P; Q |] ==> R; [| ~P; ~Q |] ==> R |] ==> R"
(fn major::prems =>
[ (rtac (major RS iffE) 1),
(REPEAT (DEPTH_SOLVE_1
(eresolve_tac ([asm_rl,impCE,notE]@prems) 1))) ]);
-val exCI = prove_goal HOL.thy "(! x. ~P(x) ==> P(a)) ==> ? x.P(x)"
+qed_goal "exCI" HOL.thy "(! x. ~P(x) ==> P(a)) ==> ? x.P(x)"
(fn prems=>
[ (rtac ccontr 1),
(REPEAT (ares_tac (prems@[exI,allI,notI,notE]) 1)) ]);
@@ -312,7 +253,7 @@
(* case distinction *)
-val case_split_thm = prove_goal HOL.thy "[| P ==> Q; ~P ==> Q |] ==> Q"
+qed_goal "case_split_thm" HOL.thy "[| P ==> Q; ~P ==> Q |] ==> Q"
(fn [p1,p2] => [cut_facts_tac [excluded_middle] 1, etac disjE 1,
etac p2 1, etac p1 1]);
@@ -323,8 +264,3 @@
fun stac th = rtac(th RS ssubst);
fun sstac ths = EVERY' (map stac ths);
fun strip_tac i = REPEAT(resolve_tac [impI,allI] i);
-
-
-end;
-
-open HOL_Lemmas;