Nat.internal_mod_eq_of_wit: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 1996-2000 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=1996&end_line=2000

import Base

def internal_mod_eq_of_wit(+a: Nat, +b: Nat, w: &k:Nat -> {Nat.add(a, k) == b : Nat}) -> {Nat.mod(a, 1n+b) == a : Nat}:
  match w:
    case (+k, e):
      %e : {Nat.mod(a, 1n+_) == a : Nat}
      Equal.trans(Nat, Nat.mod(a, 1n+Nat.add(a, k)), Nat.add(a, 0n), a, internal_mod_go_small(a, k, 0n, 0n), add_zero(a))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Exists
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_mod_go_small