Do progressive income tax lessen the income inequality?

Presuming you mean a progressive income tax as one that has higher rates of taxation on higher levels of income: I would suggest it is substantially less fair and increases inequality a lot. Even at a stable rate, people with higher incomes pay much more tax than those with less income. So, in a flat rate of say 25%, someone making say $50,000 pays $12,500. Someone making a million pays $250,000. Which one gets or uses more government and services? It probably isn't even the same...the higher income one probably uses LESS. (Private education for his kids, pays to have private services for many other things...medical, safety, transport, etc., etc., provides for his own retirement, pays for his diabled child (supporting others in doing so), etc., etc). The person with the lower income gets a great deal...probably much more of all things than they pay for, the person with the high income gets much, much less. Now, that difference becomes even more unfair and inequitable when you allow the lower earner to pay say 10% - ($5,000) and the higher earner a higher percent - say 30% or $300,000. Would take the lower earner 60 years (more than lifetime of work) and paying taxes to have ever contributed what the higher earner must do in 1 year! How much more unjust can something be? Factor in too, that the higher earner frequently pays taxes and contributes to society and the benefit to others by owning or investing in business or financial instiutions that do, that both employ people and pay many things for them...and pay tax on the money the corporation/business makes, and then again on that same earnings when it comes to them.