ElementwiseWalkProof.div_mod: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/elementwise_walk_proof.bend as ElementwiseWalkProof
Lines 61-69 of bendtorch-core@0.1.0.0/src/tensor/elementwise_walk_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_walk_proof.bend&start_line=61&end_line=69

import Base
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats

# s * (i / s) + i % s = i, for every s; at s = 0, Nat.div gives 0 and
# Nat.mod gives i.
def div_mod(+i: Nat, +s: Nat) -> {Nat.add(Nat.mul(s, Nat.div(i, s)), Nat.mod(i, s)) == i : Nat}:
  match s:
    case 0n:
      {==}
    case 1n+bp:
      %Nats.mul_comm(Nat.div(i, 1n+bp), 1n+bp) : {Nat.add(_, Nat.mod(i, 1n+bp)) == i : Nat}
      go_total(i, bp, 0n, 0n, bp, Equal.sym(Nat, bp, Nat.add(bp, 0n), add_zero_left(bp)))

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=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.div
  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=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_walk_proof.bend&name=add_zero_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_walk_proof.bend&name=go_total