Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed employing the recently proposed Grassmannian integral in N=4 super Yang-Mills theory. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.