% Universals over infinite domains are proven or refuted
% symbolically, never enumerated.

% The specification's true example: every natural is at least zero.
Query expression:
  [ForAll variable: X
          quantifier: [Natural value: X]
          body: [GreaterEqual left: X right: 0]]

% The specification's false example: not every integer is.
Query expression:
  [ForAll variable: X
          quantifier: [Integer value: X]
          body: [GreaterEqual left: X right: 0]]

% Subtype inclusion, decided symbolically: every integer is a
% rational, literally.
Query expression:
  [ForAll variable: X
          quantifier: [Integer value: X]
          body: [Rational value: X]]

% The algebra of Plus: adding zero is the identity, over all
% integers, stated flat as membership.
Query expression:
  [ForAll variable: X
          quantifier: [Integer value: X]
          body: [Plus left: X right: 0 result: X]]

% Universals over finite quantifiers just run.
Query expression:
  [ForAll variable: X
          quantifier: [Between value: X lower: 1 upper: 5]
          body: [GreaterThan left: X right: 0]]

% Existence, over a finite quantifier.
Query expression:
  [Exists variable: X
          quantifier: [Between value: X lower: 1 upper: 10]
          body: [Times left: X right: X result: 49]]