IMP_ANTISYM_RULE : thm -> thm -> thm

SYNOPSIS

Deduces equality of boolean terms from forward and backward implications.

DESCRIPTION

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 CONDITIONS

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

SEE ALSO

EQ_IMP_RULE, EQ_MP, EQ_TAC.