def internal_div_go_shift
import bend-mathlib@0.8.1.0/nat.bend as Natimport Base
867def internal_div_go_shift(n: Nat, m: Nat, +d: Nat, +r: Nat) -> {1n+Pair.fst(Nat, Nat, Nat.divmod.go(n, m, d, r)) == Pair.fst(Nat, Nat, Nat.divmod.go(n, m, 1n+d, r)) : Nat}:
868 match n m:
869 case 0n _:
870 {==}
871 case 1n+np 0n:
872 internal_div_go_shift(np, r, 1n+d, 0n)
873 case 1n+np 1n+mp:
874 internal_div_go_shift(np, mp, d, 1n+r)