\DOC GSYM

\TYPE {GSYM : thm -> thm}

\SYNOPSIS
Reverses the first equation(s) encountered in a top-down search.

\KEYWORDS
rule, symmetry, equality.

\DESCRIBE
The inference rule {GSYM} reverses the first equation(s) encountered in a
top-down search of the conclusion of the argument theorem. An equation will be
reversed iff it is not a proper subterm of another equation. If a theorem
contains no equations, it will be returned unchanged.
{
    A |- ..(s1 = s2)...(t1 = t2)..
   --------------------------------  GSYM
    A |- ..(s2 = s1)...(t2 = t1)..
}


\FAILURE
Never fails, and never loops infinitely.

\EXAMPLE
{
- arithmeticTheory.ADD;
> val it = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n)) : thm

- GSYM arithmeticTheory.ADD;
> val it = |- (!n. n = 0 + n) /\ (!m n. SUC(m + n) = (SUC m) + n) : thm
}


\SEEALSO
Drule.NOT_EQ_SYM, Thm.REFL, Thm.SYM.
\ENDDOC