reduceLib.AND

STRUCTURE

SYNOPSIS

Simplifies certain boolean conjunction expressions.

LIBRARY

reduce

DESCRIPTION

If tm corresponds to one of the forms given below, where t is an arbitrary term of type bool, then AND_CONV tm returns the corresponding theorem. Note that in the last case the conjuncts need only be alpha-equivalent rather than strictly identical.

   AND_CONV "T /\ t" = |- T /\ t = t
   AND_CONV "t /\ T" = |- t /\ T = t
   AND_CONV "F /\ t" = |- F /\ t = F
   AND_CONV "t /\ F" = |- t /\ F = F
   AND_CONV "t /\ t" = |- t /\ t = t

FAILURE

AND_CONV tm fails unless tm has one of the forms indicated above.

EXAMPLE

#AND_CONV "(x = T) /\ F";;
|- (x = T) /\ F = F

#AND_CONV "T /\ (x = T)";;
|- T /\ (x = T) = (x = T)

#AND_CONV "(?x. x=T) /\ (?y. y=T)";;
|- (?x. x = T) /\ (?y. y = T) = (?x. x = T)