def sq_mono

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64sqrt.bend:208

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64mul.bend as WM

208def sq_mono(+a: Nat, +b: Nat, +h: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_le(sq(a), sq(b)) == True{} : Bool}:
209  N.le_trans(sq(a), Nat.mul(a, b), sq(b), WM.le_mul_r(a, a, b, h), AR.mul_le(a, b, b, h))