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\DOC SYM
\TYPE {SYM : thm -> thm}
\SYNOPSIS
Swaps left-hand and right-hand sides of an equation.
\KEYWORDS
rule, symmetry, equality.
\DESCRIBE
When applied to a theorem {A |- t1 = t2}, the inference rule {SYM} returns
{A |- t2 = t1}.
{
A |- t1 = t2
-------------- SYM
A |- t2 = t1
}
\FAILURE
Fails unless the theorem is equational.
\EXAMPLE
{
# NUM_REDUCE_CONV `12 * 12`;;
val it : thm = |- 12 * 12 = 144
# SYM it;;
val it : thm = |- 144 = 12 * 12
}
\COMMENTS
The {SYM} rule requires the input theorem to be a simple equation, without
additional structure such as outer universal quantifiers. To reverse equality
signs deeper inside theorems, you may use {GSYM} instead.
\SEEALSO
GSYM, REFL, TRANS.
\ENDDOC
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