BatchedMatmulPROOF.operand_step: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedMatmulPROOF
Lines 458-474 of bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&start_line=458&end_line=474

import Base
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as Index
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith

# Term k + 1 of an operand sits one stride after term k.
def operand_step(+order: Matrix.Order, +inner: Nat, +outers: Nat, +e1: Nat, +e2: Nat, +b1: Nat, +b2: Nat, +outer: Nat, +k: Nat) ->
  {Nat.add(Matrix.stride(order, outers), Laws.operand_offset(order, inner, outers, e1, e2, b1, b2, outer, k)) ==
    Laws.operand_offset(order, inner, outers, e1, e2, b1, b2, outer, 1n+k) : Nat}:
  match order:
    case Matrix.Kept{}:
      %Equal.sym(Nat, Nat.add(Nat.mul(outer, inner), 1n+k), 1n+Nat.add(Nat.mul(outer, inner), k), Arith.add_succ(Nat.mul(outer, inner), k)) :
        {1n+Nat.add(batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(outer, inner), k)) == Nat.add(batch_base(inner, outers, e1, e2, b1, b2), _) : Nat}
      %Equal.sym(Nat, Nat.add(batch_base(inner, outers, e1, e2, b1, b2), 1n+Nat.add(Nat.mul(outer, inner), k)),
        1n+Nat.add(batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(outer, inner), k)),
        Arith.add_succ(batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(outer, inner), k))) :
        {1n+Nat.add(batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(outer, inner), k)) == _ : Nat}
      {==}
    case Matrix.Swapped{}:
      %Index.add_assoc(outers, Nat.mul(k, outers), outer) :
        {Nat.add(outers, Nat.add(batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(k, outers), outer))) == Nat.add(batch_base(inner, outers, e1, e2, b1, b2), _) : Nat}
      Nats.add_swap(outers, batch_base(inner, outers, e1, e2, b1, b2), Nat.add(Nat.mul(k, outers), outer))

Uses (11):
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/index_proofs.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=add_swap
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_LAWS.bend&name=operand_offset
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&name=batch_base
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Order
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=stride