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Universal Quantification

(forall x: A)

• Variable x bound by universal quantifier forall .
• Other syntactic forms:
  • forall _x A; /\_x A;
  • "for all x we have A"; "every x has A"; "A, for all x";
  • forall(x:A).
• Semantics: (forall x: A) is true, iff A is true for every value of x.

  A is true in every extension of the given assignment where x is mapped to a domain value.