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Definition: The truncated part of a real number is the number without its fractional part:
trunc(x) := if x < 0 then ceiling(x) else floor(x).
Proposition: For every x in R, the truncated part of the negation of x is the negation of the truncated part of x:
forall x in R: trunc(-x) = -trunc(x).
Not many nice other properties.