doc-src/Logics/LK-eg.txt

Initial revision

(**** LK examples -- process using Doc/tout LK-eg.txt ****)

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

goal LK_Rule.thy "|- EX y. ALL x. P(y)-->P(x)";
by (resolve_tac [exR] 1);
by (resolve_tac [allR] 1);
by (resolve_tac [impR] 1);
by (resolve_tac [basic] 1);
(*previous step fails!*)
by (resolve_tac [exR_thin] 1);
by (resolve_tac [allR] 1);
by (resolve_tac [impR] 1);
by (resolve_tac [basic] 1);
goal LK_Rule.thy "|- EX y. ALL x. P(y)-->P(x)";
by (best_tac LK_dup_pack 1);



goal LK_Rule.thy "|- ~ (EX x. ALL y. F(y,x) <-> ~F(y,y))";
by (resolve_tac [notR] 1);
by (resolve_tac [exL] 1);
by (resolve_tac [allL_thin] 1);
by (resolve_tac [iffL] 1);
by (resolve_tac [notL] 2);
by (resolve_tac [basic] 2);
by (resolve_tac [notR] 1);
by (resolve_tac [basic] 1);



> goal LK_Rule.thy "|- EX y. ALL x. P(y)-->P(x)";
Level 0
 |- EX y. ALL x. P(y) --> P(x)
 1.  |- EX y. ALL x. P(y) --> P(x)
> by (resolve_tac [exR] 1);
Level 1
 |- EX y. ALL x. P(y) --> P(x)
 1.  |- ALL x. P(?x) --> P(x), EX x. ALL xa. P(x) --> P(xa)
> by (resolve_tac [allR] 1);
Level 2
 |- EX y. ALL x. P(y) --> P(x)
 1. !!x.  |- P(?x) --> P(x), EX x. ALL xa. P(x) --> P(xa)
> by (resolve_tac [impR] 1);
Level 3
 |- EX y. ALL x. P(y) --> P(x)
 1. !!x. P(?x) |- P(x), EX x. ALL xa. P(x) --> P(xa)
> by (resolve_tac [basic] 1);
by: tactic failed
> by (resolve_tac [exR_thin] 1);
Level 4
 |- EX y. ALL x. P(y) --> P(x)
 1. !!x. P(?x) |- P(x), ALL xa. P(?x7(x)) --> P(xa)
> by (resolve_tac [allR] 1);
Level 5
 |- EX y. ALL x. P(y) --> P(x)
 1. !!x xa. P(?x) |- P(x), P(?x7(x)) --> P(xa)
> by (resolve_tac [impR] 1);
Level 6
 |- EX y. ALL x. P(y) --> P(x)
 1. !!x xa. P(?x), P(?x7(x)) |- P(x), P(xa)
> by (resolve_tac [basic] 1);
Level 7
 |- EX y. ALL x. P(y) --> P(x)
No subgoals!

> goal LK_Rule.thy "|- EX y. ALL x. P(y)-->P(x)";
Level 0
 |- EX y. ALL x. P(y) --> P(x)
 1.  |- EX y. ALL x. P(y) --> P(x)
> by (best_tac LK_dup_pack 1);
Level 1
 |- EX y. ALL x. P(y) --> P(x)
No subgoals!




> goal LK_Rule.thy "|- ~ (EX x. ALL y. F(y,x) <-> ~F(y,y))";
Level 0
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1.  |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
> by (resolve_tac [notR] 1);
Level 1
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. EX x. ALL y. F(y,x) <-> ~F(y,y) |-
> by (resolve_tac [exL] 1);
Level 2
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x. ALL y. F(y,x) <-> ~F(y,y) |-
> by (resolve_tac [allL_thin] 1);
Level 3
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x. F(?x2(x),x) <-> ~F(?x2(x),?x2(x)) |-
> by (resolve_tac [iffL] 1);
Level 4
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x.  |- F(?x2(x),x), ~F(?x2(x),?x2(x))
 2. !!x. ~F(?x2(x),?x2(x)), F(?x2(x),x) |-
> by (resolve_tac [notL] 2);
Level 5
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x.  |- F(?x2(x),x), ~F(?x2(x),?x2(x))
 2. !!x. F(?x2(x),x) |- F(?x2(x),?x2(x))
> by (resolve_tac [basic] 2);
Level 6
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x.  |- F(x,x), ~F(x,x)
> by (resolve_tac [notR] 1);
Level 7
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
 1. !!x. F(x,x) |- F(x,x)
> by (resolve_tac [basic] 1);
Level 8
 |- ~(EX x. ALL y. F(y,x) <-> ~F(y,y))
No subgoals!