What makes you say inflation wouldn't double? It's not clear to me that there's a linear relation between money supply/money velocity and inflation. In addition, I think there's a large psychological component to inflation: people spending money sooner than they would otherwise, i.e., quick buy it now before prices go up more; and, demanding increases in wages to match the expected increases in prices.
I mean, inflation wouldn't double as a result of giving the bottom 25% additional money, but unless there was a matching increase in the supply of goods and services, the additional money would make prices rise.
I dont like the recent inflation, but as someone one the upper end of the income distribution (likely true of many HN readers), my life isn't fucked up by it. Merely my discretionary income.