Interval exactness of a tent-map core

If $\sqrt{2}<s\le 2$, every nondegenerate subinterval of $A=[1-s,1]$ eventually maps onto $A$. Away from the critical point, lengths multiply by $s$; one fold loses at most a factor of two. If an interval and its image both contain zero, its second image is $A$. Otherwise every two steps increase length by at least $s^2/2>1$, which cannot continue inside bounded $A$. Applying the intermediate value theorem to an interval that covers itself then gives a periodic point in every subinterval.

// Target: dynamical-systems.bigb