'inadvertently-proven' originates from the combination of 'inadvertently' and 'proven'. 'Inadvertently' comes from Latin, specifically the word 'inadvertentem', where 'in-' meant 'not' and 'advertentem' meant 'turning the mind to'. 'Proven' is the past participle of 'prove', which comes from Latin 'probare', meaning 'to test or prove'.

'Inadvertently' changed from the Latin word 'inadvertentem' and eventually became the modern English word 'inadvertently'. 'Proven' evolved from the Latin 'probare' through Old French 'prover', and eventually became the modern English word 'proven'.

Initially, 'inadvertently' meant 'not turning the mind to', but over time it evolved into its current meaning of 'unintentionally'. 'Proven' has largely retained its original meaning of 'tested or demonstrated to be true'.