The equivalence between the definition of supermodularity and its calculus formulation is sometimes called Topkis' characterization theorem. See Milgrom, Paul; Roberts, John (1990). "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities". Econometrica. 58 (6): 1255–1277 [p. 1261]. doi:10.2307/2938316. JSTOR2938316.
The equivalence between the definition of supermodularity and its calculus formulation is sometimes called Topkis' characterization theorem. See Milgrom, Paul; Roberts, John (1990). "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities". Econometrica. 58 (6): 1255–1277 [p. 1261]. doi:10.2307/2938316. JSTOR2938316.