$$x>0\implies-x<0$$
I thought about using the axioms of multiplication with $x\cdot (-1) = -x$
but I am kind of stuck there.
2026-03-27 23:32:13.1774654333
How can I prove if $x>0$ then $-x<0$?
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$If x>0 then 0=-x+x>-x+0 so that -x<0. If x<0 then 0=-x+x<-x+0 so that -x>0$