def div_of

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/arith.bend:31

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/lemmas/proofs/natural_division.bend as ND

31# the quotient and remainder are unique
32def div_of(+q: Nat, +bp: Nat, +r: Nat, +h: {Nat.is_lt(r, 1n+bp) == True{} : Bool}) -> {Nat.div(Nat.add(Nat.mul(q, 1n+bp), r), 1n+bp) == q : Nat}:
33  ND.quotient(q, bp, r, N.lt_succ_le(r, bp, h))