TransposePROOF.matrix_source: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend as TransposePROOF
Lines 210-235 of bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend&start_line=210&end_line=235

import Base
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend as MatrixIndex

def matrix_source(+rows: U32, +columns: U32, +j: Nat, +l: Nat,
  +j_below: {Nat.is_lt(j, U32.to_nat(columns)) == True{} : Bool},
  +l_below: {Nat.is_lt(l, U32.to_nat(rows)) == True{} : Bool},
  +exact: {U32.to_nat(U32.from_nat(Nat.add(Nat.mul(j, U32.to_nat(rows)), l))) == Nat.add(Nat.mul(j, U32.to_nat(rows)), l) : Nat}) ->
  {transposed_source([rows, columns], U32.from_nat(Nat.add(Nat.mul(j, U32.to_nat(rows)), l))) ==
    Some{U32.from_nat(Nat.add(Nat.mul(l, U32.to_nat(columns)), j))} : Maybe<&2, U32>}:
  +r = U32.to_nat(rows)
  +c = U32.to_nat(columns)
  +i = Nat.add(Nat.mul(j, r), l)
  %Equal.sym(Nat, U32.to_nat(U32.from_nat(i)), i, exact) :
    {Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(Matrix.column_of(r, _))), Nat.mul(c, 1n)),
       Nat.add(Nat.mul(U32.to_nat(U32.from_nat(Matrix.row_of(r, U32.to_nat(U32.from_nat(i))))), 1n), 0n)))} ==
      Some{U32.from_nat(Nat.add(Nat.mul(l, c), j))} : Maybe<&2, U32>}
  %Equal.sym(Nat, U32.to_nat(U32.from_nat(i)), i, exact) :
    {Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(Matrix.column_of(r, i))), Nat.mul(c, 1n)),
       Nat.add(Nat.mul(U32.to_nat(U32.from_nat(Matrix.row_of(r, _))), 1n), 0n)))} ==
      Some{U32.from_nat(Nat.add(Nat.mul(l, c), j))} : Maybe<&2, U32>}
  %Equal.sym(Nat, Matrix.column_of(r, i), l, MatrixIndex.column_at(j, l, r, l_below)) :
    {Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(_)), Nat.mul(c, 1n)),
       Nat.add(Nat.mul(U32.to_nat(U32.from_nat(Matrix.row_of(r, i))), 1n), 0n)))} ==
      Some{U32.from_nat(Nat.add(Nat.mul(l, c), j))} : Maybe<&2, U32>}
  %Equal.sym(Nat, Matrix.row_of(r, i), j, MatrixIndex.row_at(j, l, r, l_below)) :
    {Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(l)), Nat.mul(c, 1n)),
       Nat.add(Nat.mul(U32.to_nat(U32.from_nat(_)), 1n), 0n)))} ==
      Some{U32.from_nat(Nat.add(Nat.mul(l, c), j))} : Maybe<&2, U32>}
  swapped_offset(rows, columns, j, l, j_below, l_below)

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=column_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=row_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=column_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=row_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend&name=swapped_offset
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend&name=transposed_source