The factorization command extracts a formula
that is a common factor in both sub-formulae.
Some of these are inverses of distribution steps.
Unusually, these steps are organized by the syntax of the result,
not that of the original formula.
Contents of this page
Conjunctions
p1 p2 (p1 p3) | | p1 (p2 p3) |
p1 p3 (p2 p3) | | p1 p2 p3 |
p1 p2 p1 p3 | | p1 (p2 p3) |
p1 p3 p2 p3 | | (p1 p2) p3 |
Disjunctions
p1 p2 (p1 p3) | | p1 (p2 p3) |
p1 p3 (p2 p3) | | p1 p2 p3 |
(p1 p2) (p1 p3) | | p1 p2 p3 |
(p1 p3) (p2 p3) | | p1 p2 p3 |
Implications
(p1 p2) (p1 p3) | | p1 p2 p3 |
(p1 p3) (p2 p3) | | p1 p2 p3 |
p1 p2 p1 p3 | | p1 (p2 p3) |
Universal quantifications
( s p1) ( s p2) | | s p1 p2 |
( s p1) ( s p2) | | s p1 p2 where s has only == decs |
( s p1) ( s p2) | | s p1 p2 where s has only == decs |
Existential quantifications
( s p1) ( s p2) | | s p1 p2 where s has only == decs |
( s p1) ( s p2) | | s p1 p2 |
( s p1) ( s p2) | | s p1 p2 where s has only == decs |
Unique existential quantifications
( 1 s p1) ( 1 s p2) | | 1 s p1 p2 where s has only == decs |
( 1 s p1) ( 1 s p2) | | 1 s p1 p2 where s has only == decs |
( 1 s p1) ( 1 s p2) | | 1 s p1 p2 where s has only == decs |
Tactic example
"factorization" p4 p5
This example applies the factorization command
to predicates p4 and p5.
IT 5-Apr-2000