FORALL_CONJ_ONCE_CONV : conv
STRUCTURE
unwindLib
SYNOPSIS
Moves a single universal quantifier down through a tree of conjunctions.
LIBRARY
unwind
DESCRIPTION
FORALL_CONJ_ONCE_CONV "!x. t1 /\ ... /\ tn" returns the theorem: 
   |- !x. t1 /\ ... /\ tn = (!x. t1) /\ ... /\ (!x. 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 body of the term need not be a conjunction.
EXAMPLE
#FORALL_CONJ_ONCE_CONV "!x. ((x \/ a) /\ (x \/ b)) /\ (x \/ c)";;
|- (!x. ((x \/ a) /\ (x \/ b)) /\ (x \/ c)) =
   ((!x. x \/ a) /\ (!x. x \/ b)) /\ (!x. x \/ c)

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

#FORALL_CONJ_ONCE_CONV "!x. ((x \/ a) /\ (y \/ b)) /\ (x \/ c)";;
|- (!x. ((x \/ a) /\ (y \/ b)) /\ (x \/ c)) =
   ((!x. x \/ a) /\ (!x. y \/ b)) /\ (!x. x \/ c)
SEEALSO
CONJ_FORALL_ONCE_CONV, FORALL_CONJ_CONV, CONJ_FORALL_CONV, FORALL_CONJ_RIGHT_RULE, CONJ_FORALL_RIGHT_RULE
HOL  Kananaskis-13