def jmin

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64light.bend:107

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW

107def jmin(+q: Nat, +r: Nat) -> {SW.jam(q, SF.b2n(Bool.not(Nat.is_eq(r, 0n)))) == SW.jam(q, r) : Nat}:
108  match r:
109    case 0n:
110      {==}
111    case 1n+ +rp:
112      Equal.cong(Nat, Nat, z => Nat.add(Nat.mul(2n, Nat.div(q, 2n)), Nat.max(Nat.mod(q, 2n), z)), 1n, Nat.min(1n+rp, 1n), Equal.sym(Nat, 1n+Nat.min(rp, 0n), 1n, Equal.cong(Nat, Nat, z => 1n+z, Nat.min(rp, 0n), 0n, minz(rp))))