Inverse.mod_self: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend as Inverse
Lines 136-138 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&start_line=136&end_line=138

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend as LC

def mod_self(+mp: Nat) -> {Nat.mod(1n+mp, 1n+mp) == 0n : Nat}:
  %Equal.sym(Nat, 1n+mp, Nat.add(Nat.mul(1n, 1n+mp), 0n), Equal.trans(Nat, 1n+mp, Nat.mul(1n, 1n+mp), Nat.add(Nat.mul(1n, 1n+mp), 0n), Equal.sym(Nat, Nat.mul(1n, 1n+mp), 1n+mp, LC.one_mul(1n+mp)), Equal.sym(Nat, Nat.add(Nat.mul(1n, 1n+mp), 0n), Nat.mul(1n, 1n+mp), A.add_zero(Nat.mul(1n, 1n+mp))))) : {Nat.mod(_, 1n+mp) == 0n : Nat}
  R.mod_of(1n, mp, 0n, {==})

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=mod_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend&name=one_mul