the.com/derivation

Proof wearing a trench coat, revealing itself one logical step at a time.

means The step-by-step chain of reasoning (or word history) that shows how you got from a starting point to a conclusion — the 'show your work' of logic or language.

from From Latin derivare, 'to lead or draw off,' originally used of water: diverting a stream (rivus, 'river' or 'brook') away from its main channel via a side-channel (de-, 'away from' + rivus). The image carried into Old French and then English, where by the 1500s it described tracing how a word, idea, or conclusion had been 'channeled off' from an original source — knowledge flowing step by step from its headwaters to wherever it ends up.

not a proof
proof shows truth, derivation shows the path
etymology
from Latin rivus, a stream branching off
logic use
each line must follow by a named rule
linguistics twist
also means birthing cat from feline, suffix style
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