MatmulPROOF.right_flat: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 1351-1366 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=1351&end_line=1366

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

def right_flat(+right: Shape.Shape, +inner: U32, +right_inner: U32, +columns: U32, +column: Nat, +k: Nat,
  +re: {Shape.dimensions(right) == [right_inner, columns] : List<&2, U32>},
  +compatible: {U32.to_nat(inner) == U32.to_nat(right_inner) : Nat},
  +column_below: {Nat.is_lt(column, U32.to_nat(columns)) == True{} : Bool}, +below: {Nat.is_lt(k, U32.to_nat(inner)) == True{} : Bool}) ->
  {ShapeLaws.index_result(right, Shape.flatten_checked(right, [U32.from_nat(k), U32.from_nat(column)])) ==
    Some{Matrix.right_index(U32.to_nat(columns), column, k)} : Maybe<&2, U32>}:
  +k_exact = MatrixIndex.word_below(k, inner, below)
  +column_exact = MatrixIndex.word_below(column, columns, column_below)
  Equal.trans(Maybe<&2, U32>, ShapeLaws.index_result(right, Shape.flatten_checked(right, [U32.from_nat(k), U32.from_nat(column)])),
    Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(k)), U32.to_nat(columns)), U32.to_nat(U32.from_nat(column))))},
    Some{U32.from_nat(Nat.add(Nat.mul(k, U32.to_nat(columns)), column))},
    MatrixIndex.flat_pair(right, right_inner, columns, U32.from_nat(k), U32.from_nat(column), re,
      MatrixIndex.lt_same(U32.to_nat(U32.from_nat(k)), k, U32.to_nat(right_inner), k_exact,
        MatrixIndex.lt_bound(k, U32.to_nat(inner), U32.to_nat(right_inner), compatible, below)),
      MatrixIndex.lt_same(U32.to_nat(U32.from_nat(column)), column, U32.to_nat(columns), column_exact, column_below)),
    MatrixIndex.index_same(U32.to_nat(U32.from_nat(k)), U32.to_nat(U32.from_nat(column)), k, column, U32.to_nat(columns), k_exact, column_exact))

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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/shape/LAWS.bend&name=index_result
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=flatten_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=right_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=flat_pair
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=index_same
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=lt_bound
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=lt_same
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=word_below