This statement represents standard microeconomic theory regarding producer behavior and cost functions, which are fundamental mathematical properties by definition.
The claim states two standard microeconomic propositions: that cost functions are concave in input prices (a mathematical consequence of cost minimization) and that input demand is downward sloping (implied by Shephard's lemma or Hotelling's lemma via the negative semi-definiteness of the substitution matrix). These are definitional properties of neoclassical producer theory. Following the instructions, trivially true properties or core microeconomic definitions of this kind are classified as COMMON_KNOWLEDGE, requiring no citations.