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CONJ_FORALL_ONCE_CONV                                      (unwindLib)
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CONJ_FORALL_ONCE_CONV : conv

SYNOPSIS
Moves a single universal quantifier up through a tree of conjunctions.

LIBRARY
unwind

DESCRIBE
{CONJ_FORALL_ONCE_CONV "(!x. t1) /\ ... /\ (!x. tn)"} returns the theorem:

   |- (!x. t1) /\ ... /\ (!x. tn) = !x. t1 /\ ... /\ tn

where the original term can be an arbitrary tree of conjunctions. The
structure of the tree is retained in both sides of the equation.

FAILURE
Fails if the argument term is not of the required form. The term need not be a
conjunction, but if it is every conjunct must be universally quantified with
the same variable.

EXAMPLE

#CONJ_FORALL_ONCE_CONV "((!x. x \/ a) /\ (!x. x \/ b)) /\ (!x. x \/ c)";;
|- ((!x. x \/ a) /\ (!x. x \/ b)) /\ (!x. x \/ c) =
   (!x. ((x \/ a) /\ (x \/ b)) /\ (x \/ c))

#CONJ_FORALL_ONCE_CONV "!x. x \/ a";;
|- (!x. x \/ a) = (!x. x \/ a)

#CONJ_FORALL_ONCE_CONV "((!x. x \/ a) /\ (!y. y \/ b)) /\ (!x. x \/ c)";;
evaluation failed     CONJ_FORALL_ONCE_CONV


SEEALSO
unwindLib.FORALL_CONJ_ONCE_CONV, unwindLib.CONJ_FORALL_CONV,
unwindLib.FORALL_CONJ_CONV, unwindLib.CONJ_FORALL_RIGHT_RULE,
unwindLib.FORALL_CONJ_RIGHT_RULE.

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