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\DOC IMP_ANTISYM_RULE
\TYPE {IMP_ANTISYM_RULE : thm -> thm -> thm}
\SYNOPSIS
Deduces equality of boolean terms from forward and backward implications.
\KEYWORDS
rule, implication, equality.
\DESCRIBE
When applied to the theorems {A1 |- t1 ==> t2} and {A2 |- t2 ==> t1}, the
inference rule {IMP_ANTISYM_RULE} returns the theorem {A1 u A2 |- t1 <=> t2}.
{
A1 |- t1 ==> t2 A2 |- t2 ==> t1
------------------------------------- IMP_ANTISYM_RULE
A1 u A2 |- t1 <=> t2
}
\FAILURE
Fails unless the theorems supplied are a complementary implicative
pair as indicated above.
\EXAMPLE
{
# let th1 = TAUT `p /\ q ==> q /\ p`
and th2 = TAUT `q /\ p ==> p /\ q`;;
val th1 : thm = |- p /\ q ==> q /\ p
val th2 : thm = |- q /\ p ==> p /\ q
# IMP_ANTISYM_RULE th1 th2;;
val it : thm = |- p /\ q <=> q /\ p
}
\SEEALSO
EQ_IMP_RULE, EQ_MP, EQ_TAC.
\ENDDOC
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