fact: Definition natnat_to_nat2_inv n := let m := Nat.sqrt n.*2 in let s := if m * m.+1 <= n.*2 then m else m.-1 in let a := n - 'C(s.+1, 2) in (a, s-a).
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)