I think you always need the condition. Just saying "for all x"
doesn't make any sense. You have to have "for all x in some set".
By the way, it's just a semantics things, but expr should really be
called cond, since it needs to be a boolean condition, not just some
generic expression.
Aaron Meurer
On Wed, Mar 28, 2012 at 3:19 PM, sachin004 <sachin.iruk...@gmail.com> wrote:
> Implementation of universal quantifiers
>
> Universal Quantification: Function: for_all(expr,variables,condition)
>
> · ∀ xexpr which says that expr holds for all values of x for this the
> function looks like for_all(expr,var) where var=Tuple(x)
>
> this returns an assertion based on the expr and the values of x.
>
> · ∀{x1,x2,...}expr which says that expr holds for all values of x for
> this the function looks like for_all(expr,var) where var=(x1,x2,x3….) this
> returns an assertion based on the expr and the values of x1,x2,x3...
>
> · ∀x,condexpr which says that expr holds for all values of x which
> satisfy the condition for this the function looks like for_all(expr,var)
> where var=(x1,x2,x3….) this returns an assertion based on the expr and the
> values of x1,x2,x3...
>
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