The expression under the quantifier must have the form , otherwise the result is False in any case.
There is a special form of the ForAll-quantifier that performs componentwise operations:
![[Graphics:LogicalQuantifiersgr2.gif]](LogicalQuantifiersgr2.gif)
![[Graphics:LogicalQuantifiersgr1.gif]](LogicalQuantifiersgr1.gif)
![[Graphics:LogicalQuantifiersgr16.gif]](LogicalQuantifiersgr16.gif)
, otherwise the result is False in any case.![[Graphics:LogicalQuantifiersgr3.gif]](LogicalQuantifiersgr3.gif)
![[Graphics:LogicalQuantifiersgr4.gif]](LogicalQuantifiersgr4.gif)
![[Graphics:LogicalQuantifiersgr5.gif]](LogicalQuantifiersgr5.gif)
![[Graphics:LogicalQuantifiersgr6.gif]](LogicalQuantifiersgr6.gif)
![[Graphics:LogicalQuantifiersgr7.gif]](LogicalQuantifiersgr7.gif)
![[Graphics:LogicalQuantifiersgr8.gif]](LogicalQuantifiersgr8.gif)
![[Graphics:LogicalQuantifiersgr9.gif]](LogicalQuantifiersgr9.gif)
![[Graphics:LogicalQuantifiersgr10.gif]](LogicalQuantifiersgr10.gif)
![[Graphics:LogicalQuantifiersgr11.gif]](LogicalQuantifiersgr11.gif)
![[Graphics:LogicalQuantifiersgr12.gif]](LogicalQuantifiersgr12.gif)
![[Graphics:LogicalQuantifiersgr13.gif]](LogicalQuantifiersgr13.gif)
![[Graphics:LogicalQuantifiersgr14.gif]](LogicalQuantifiersgr14.gif)
![[Graphics:LogicalQuantifiersgr15.gif]](LogicalQuantifiersgr15.gif)
![[Graphics:LogicalQuantifiersgr17.gif]](LogicalQuantifiersgr17.gif)
![[Graphics:LogicalQuantifiersgr18.gif]](LogicalQuantifiersgr18.gif)
![[Graphics:LogicalQuantifiersgr19.gif]](LogicalQuantifiersgr19.gif)
![[Graphics:LogicalQuantifiersgr20.gif]](LogicalQuantifiersgr20.gif)
![[Graphics:LogicalQuantifiersgr21.gif]](LogicalQuantifiersgr21.gif)
![[Graphics:LogicalQuantifiersgr22.gif]](LogicalQuantifiersgr22.gif)