doc-src/Intro/deriv.txt

fixed arities and restored changes that had gone missing

(* Deriving an inference rule *)

Pretty.setmargin 72;  (*existing macros just allow this margin*)
print_depth 0;


val [major,minor] = goal IFOL.thy
    "[| P&Q;  [| P; Q |] ==> R |] ==> R";
prth minor;
by (resolve_tac [minor] 1);
prth major;
prth (major RS conjunct1);
by (resolve_tac [major RS conjunct1] 1);
prth (major RS conjunct2);
by (resolve_tac [major RS conjunct2] 1);
prth (topthm());
val conjE = prth(result());


- val [major,minor] = goal Int_Rule.thy
=     "[| P&Q;  [| P; Q |] ==> R |] ==> R";
Level 0
R
 1. R
val major = Thm {hyps=#,maxidx=#,prop=#,sign=#} : thm
val minor = Thm {hyps=#,maxidx=#,prop=#,sign=#} : thm
- prth minor;
[| P; Q |] ==> R  [[| P; Q |] ==> R]
- by (resolve_tac [minor] 1);
Level 1
R
 1. P
 2. Q
- prth major;
P & Q  [P & Q]
- prth (major RS conjunct1);
P  [P & Q]
- by (resolve_tac [major RS conjunct1] 1);
Level 2
R
 1. Q
- prth (major RS conjunct2);
Q  [P & Q]
- by (resolve_tac [major RS conjunct2] 1);
Level 3
R
No subgoals!
- prth (topthm());
R  [P & Q, P & Q, [| P; Q |] ==> R]
- val conjE = prth(result());
[| ?P & ?Q; [| ?P; ?Q |] ==> ?R |] ==> ?R
val conjE = Thm {hyps=#,maxidx=#,prop=#,sign=#} : thm


(*** Derived rules involving definitions ***)

(** notI **)

val prems = goal Int_Rule.thy "(P ==> False) ==> ~P";
prth not_def;
by (rewrite_goals_tac [not_def]);
by (resolve_tac [impI] 1);
by (resolve_tac prems 1);
by (assume_tac 1);
val notI = prth(result());

val prems = goalw Int_Rule.thy [not_def]
    "(P ==> False) ==> ~P";


- prth not_def;
~?P == ?P --> False
- val prems = goal Int_Rule.thy "(P ==> False) ==> ~P";
Level 0
~P
 1. ~P
- by (rewrite_goals_tac [not_def]);
Level 1
~P
 1. P --> False
- by (resolve_tac [impI] 1);
Level 2
~P
 1. P ==> False
- by (resolve_tac prems 1);
Level 3
~P
 1. P ==> P
- by (assume_tac 1);
Level 4
~P
No subgoals!
- val notI = prth(result());
(?P ==> False) ==> ~?P
val notI = # : thm

- val prems = goalw Int_Rule.thy [not_def]
=     "(P ==> False) ==> ~P";
Level 0
~P
 1. P --> False


(** notE **)

val [major,minor] = goal Int_Rule.thy "[| ~P;  P |] ==> R";
by (resolve_tac [FalseE] 1);
by (resolve_tac [mp] 1);
prth (rewrite_rule [not_def] major);
by (resolve_tac [it] 1);
by (resolve_tac [minor] 1);
val notE = prth(result());

val [major,minor] = goalw Int_Rule.thy [not_def]
    "[| ~P;  P |] ==> R";
prth (minor RS (major RS mp RS FalseE));
by (resolve_tac [it] 1);


val prems = goalw Int_Rule.thy [not_def]
    "[| ~P;  P |] ==> R";
prths prems;
by (resolve_tac [FalseE] 1);
by (resolve_tac [mp] 1);
by (resolve_tac prems 1);
by (resolve_tac prems 1);
val notE = prth(result());


- val [major,minor] = goal Int_Rule.thy "[| ~P;  P |] ==> R";
Level 0
R
 1. R
val major = # : thm
val minor = # : thm
- by (resolve_tac [FalseE] 1);
Level 1
R
 1. False
- by (resolve_tac [mp] 1);
Level 2
R
 1. ?P1 --> False
 2. ?P1
- prth (rewrite_rule [not_def] major);
P --> False  [~P]
- by (resolve_tac [it] 1);
Level 3
R
 1. P
- by (resolve_tac [minor] 1);
Level 4
R
No subgoals!
- val notE = prth(result());
[| ~?P; ?P |] ==> ?R
val notE = # : thm
- val [major,minor] = goalw Int_Rule.thy [not_def]
=     "[| ~P;  P |] ==> R";
Level 0
R
 1. R
val major = # : thm
val minor = # : thm
- prth (minor RS (major RS mp RS FalseE));
?P  [P, ~P]
- by (resolve_tac [it] 1);
Level 1
R
No subgoals!




- goal Int_Rule.thy "[| ~P;  P |] ==> R";
Level 0
R
 1. R
- prths (map (rewrite_rule [not_def]) it);
P --> False  [~P]

P  [P]

- val prems = goalw Int_Rule.thy [not_def]
=     "[| ~P;  P |] ==> R";
Level 0
R
 1. R
val prems = # : thm list
- prths prems;
P --> False  [~P]

P  [P]

- by (resolve_tac [mp RS FalseE] 1);
Level 1
R
 1. ?P1 --> False
 2. ?P1
- by (resolve_tac prems 1);
Level 2
R
 1. P
- by (resolve_tac prems 1);
Level 3
R
No subgoals!
- val notE = prth(result());
[| ~?P; ?P |] ==> ?R
val notE = # : thm