def gcd_dvd_left
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend as Gcdimport Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend as M
119def gcd_dvd_left(+a: Nat, +b: Nat) -> {a == Nat.mul(wl(ws(b, a, b)), M.gcd(a, b)) : Nat}:
120 both_l(a, b, M.gcd(a, b), ws(b, a, b), gcd_both(b, a, b, N.le_refl(b)))
Uses (8)
Used by (7)
- bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm:lcm_pos
- bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm:dvd_lcm_left
- bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm:gcd_mul_lcm
- bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm:gcd_mul_pos
- bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm:lcm_dvd_pos
- …