reduceLib.IMP

STRUCTURE

SYNOPSIS

Simplifies certain implicational expressions.

LIBRARY

reduce

DESCRIPTION

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

   IMP_CONV "T ==> t" = |- T ==> t = t
   IMP_CONV "t ==> T" = |- t ==> T = T
   IMP_CONV "F ==> t" = |- F ==> t = T
   IMP_CONV "t ==> F" = |- t ==> F = ~t
   IMP_CONV "t ==> t" = |- t ==> t = T

FAILURE

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

EXAMPLE

#IMP_CONV "T ==> F";;
|- T ==> F = F

#IMP_CONV "F ==> x";;
|- F ==> x = T

#IMP_CONV "(!z:(num)list. z = z) ==> (!x:(num)list. x = x)";;
|- (!z. z = z) ==> (!x. x = x) = T