MatmulPROOF.inner_left: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 1246-1266 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=1246&end_line=1266

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/storage/arith.bend as Arith

def inner_left(+left: Shape.Shape, +right: Shape.Shape, +dims: List<&2, U32>,
  -same: {dims == Shape.dimensions(left) : List<&2, U32>},
  -rows: U32, -inner: U32, -right_inner: U32, -columns: U32,
  left_matrix: {dims == [rows, inner] : List<&2, U32>},
  right_matrix: {Shape.dimensions(right) == [right_inner, columns] : List<&2, U32>},
  mismatch: {U32.to_nat(inner) != U32.to_nat(right_inner) : Nat}) ->
  {Matrix.plan_left(left, right, dims, same) == Fail{Matrix.InnerDimensionMismatch{}} : Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>}:
  match dims:
    case +r <> +i <> Nil{}:
      inner_right(left, right, r, i, Equal.sym(List<&2, U32>, [r, i], Shape.dimensions(left), same), Shape.dimensions(right), {==},
        inner, right_inner, columns, right_matrix,
        Equal.cong(List<&2, U32>, Nat, second_nat, [r, i], [rows, inner], left_matrix), mismatch)
    case Nil{}:
      Empty.absurd({Matrix.plan_left(left, right, Nil{}, same) == Fail{Matrix.InnerDimensionMismatch{}} : Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>},
        Arith.clash(Equal.cong(List<&2, U32>, Bool, xs => Nat.is_eq(Shape.rank_dimensions(xs), 2n), Nil{}, [rows, inner], left_matrix)))
    case +x <> Nil{}:
      Empty.absurd({Matrix.plan_left(left, right, [x], same) == Fail{Matrix.InnerDimensionMismatch{}} : Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>},
        Arith.clash(Equal.cong(List<&2, U32>, Bool, xs => Nat.is_eq(Shape.rank_dimensions(xs), 2n), [x], [rows, inner], left_matrix)))
    case +x <> +y <> +z <> +t:
      Empty.absurd({Matrix.plan_left(left, right, x <> y <> z <> t, same) == Fail{Matrix.InnerDimensionMismatch{}} : Result<&2, &2, Matrix.Error, Matrix.Plan<left, right>>},
        Arith.clash(Equal.cong(List<&2, U32>, Bool, xs => Nat.is_eq(Shape.rank_dimensions(xs), 2n), x <> y <> z <> t, [rows, inner], left_matrix)))

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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/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=rank_dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=plan_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=inner_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=second_nat