def ilt

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqa.bend:22

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend as SQ

22def ilt(+n: Nat) -> {Nat.is_lt(n, Nat.mul(1n+M.isqrt(n), 1n+M.isqrt(n))) == True{} : Bool}:
23  L.subst(Nat, z => {Nat.is_lt(n, z) == True{} : Bool}, Nat.pow(1n+M.isqrt(n), 2n), Nat.mul(1n+M.isqrt(n), 1n+M.isqrt(n)), sqm(1n+M.isqrt(n)), SQ.lt_succ_isqrt(n))