Have a statement that seems true by geometric inspection but I can't seem to prove it using triangle/reverse triangle inequality.
$|x|+|y|\leq 1 \implies|1-x|+|1-y|\geq 1$
2026-02-23 10:03:24.1771841004
$|x|+|y|\leq 1$ implies $|1-x|+|1-y|\geq 1$
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By the triangle inequality and then the fact that $|x|+|y|\leq 1$ $$ 2 = |1-x + x + 1-y + y| \leq |1-x| + |x| + |1-y| + |y| \\ \leq 1 + |1-x| + |1-y| $$ and your inequality follows by subtracting $1$ on both sides.