def internal_mod_go_d
import bend-mathlib@0.8.1.0/nat.bend as Natimport Base
2034def internal_mod_go_d(n: Nat, m: Nat, -d: Nat, -e: Nat, r: Nat) -> {Pair.snd(Nat, Nat, Nat.divmod.go(n, m, d, r)) == Pair.snd(Nat, Nat, Nat.divmod.go(n, m, e, r)) : Nat}:
2035 match n m:
2036 case 0n _:
2037 {==}
2038 case 1n+np 0n:
2039 internal_mod_go_d(np, r, 1n+d, 1n+e, 0n)
2040 case 1n+np 1n+mp:
2041 internal_mod_go_d(np, mp, d, e, 1n+r)