The phrase "demonstrate the compatibility" is correct and usable in written English.
You can use it when discussing how two components, people, ideas, products, etc. can work together harmoniously. For example: "The architects were able to demonstrate the compatibility of traditional aesthetics with modern building materials."
These results clearly demonstrate the compatibility of the BC membranes used in this study with osteoblasts.
They also demonstrate the compatibility and complementarity of these species when grown together.
Results are compared with BF2+ implantations made on an AXCELIS NV-8200P beam line implanter and demonstrate the compatibility with semiconductor requirements.
Those wishing to demonstrate the compatibility between process theism and Jewish and Christian Scripture commonly follow David Griffin's arguments that the Bible neither requires nor implies an absolute beginning of the universe (Griffin 2001b, 109 114).
In this report we demonstrate the compatibility of zirconium acetylacetonate (ZrAcac) electron extracting layers in both regular and inverted small molecule OPV cells.
The electrical characteristics of the as prepared junctions reveal the successful patterning and demonstrate the compatibility of the process sequence steps with the organic materials.
You write, in commentary, "it is astounding that this passage was written with the intent of demonstrating the compatibility of faith and reason".
The full-scale beams demonstrated the compatibility of the repaired system by providing data on authentic field conditions.
In doing so it demonstrates the compatibility of these approaches through the careful inspection of a specific empirical case study.
The results of DSC, XRD and FT-IR studies demonstrated the compatibility between the drug and the components.
The full-scale beams demonstrated the compatibility of the repair system by providing real data on the effectiveness of the repair material.
