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Built-in Functions

Algebraic Computation

Formula Manipulation

ForAll

Usage

• ForAll[x, expr] represents the statement that expr is True for all values of x.
• ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond.
• ForAll[{, , ... }, expr] states that expr is True for all values of all the .

Notes

• ForAll[x, expr] can be entered as

. The character

can be entered as

fa

or \[ForAll]. The variable x is given as a subscript.

• ForAll[x, cond, expr] can be entered as

.

• In StandardForm, ForAll[x, expr] is output as

.

• ForAll[x, cond, expr] is output as

.

• ForAll can be used in such functions as Reduce, Resolve and FullSimplify.

• The condition cond is often used to specify the domain of a variable, as in x

Integers.

• ForAll[x, cond, expr] is equivalent to ForAll[x, Implies[cond, expr]].

• ForAll[{

,

, ... }, ... ] is equivalent to

.

• The value of x in ForAll[x, expr] is taken to be localized, as in Block.

• See Section 3.4.11.

• See also: Exists, Resolve, Reduce, Element, Blank, SolveAlways.

• New in Version 5.

Further Examples

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