If separated subsystem properties must mirror composite-system properties across all observables, this constitutes precisely the kind of global value assignment Kochen-Specker prohibits.

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Composite system(quantum mechanics): Multiple things treated together as a single, interconnected whole—in this case, the electron, the measuring device, and the surrounding environment all considered as one system.
Kochen-Specker theorem(the main subject of the statement): A mathematical proof from quantum physics showing that you can't assign definite values to all quantum properties at once in a way that matches what experiments actually show.
global value assignment(a specific way of assigning properties in quantum mechanics): Assigning definite, fixed values to all properties of a system at the same time, like saying 'every particle has a definite position and speed right now.'
mirror (as a verb)(meaning subsystem properties should match composite-system properties): To match or reflect exactly, like looking in a mirror and seeing your exact image.
observables(gauge theory): Gauge-invariant quantities in a gauge theory
properties(Contrasted with substances as ontologically dependent entities.): Entities that depend for their existence on substances, being properties of individual objects.
subsystem(describing properties of parts of a physical system): A smaller part of a larger system that can be studied on its own, like examining one instrument in an orchestra rather than the whole band.

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