AxisAlgebra.facts_3: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend as AxisAlgebra
Lines 2159-2254 of bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&start_line=2159&end_line=2254

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend as Axis

def facts_3(+axes: List<&2, Nat>, accepted: {True{} == Axis.valid(3n, axes) : Bool}) -> Facts<3n, axes>:
  match axes:
    case Nil{}:
      Empty.absurd(Facts<3n, Nil{}>, Shape.clash(accepted))
    case +a0 <> Nil{}:
      Empty.absurd(Facts<3n, a0 <> Nil{}>, Shape.clash(accepted))
    case +a0 <> +a1 <> Nil{}:
      Empty.absurd(Facts<3n, a0 <> a1 <> Nil{}>, Shape.clash(accepted))
    case 0n <> 0n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 0n, 0n]>, Shape.clash(accepted))
    case 0n <> 0n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 0n, 1n]>, Shape.clash(accepted))
    case 0n <> 0n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 0n, 2n]>, Shape.clash(accepted))
    case 0n <> 0n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 0n <> 0n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(0n <> 0n <> (3n+p) <> Nil{}, 3n), Axis.unique(0n <> 0n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 0n <> 0n <> (3n+p) <> Nil{}), accepted)))))
    case 0n <> 1n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 1n, 0n]>, Shape.clash(accepted))
    case 0n <> 1n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 1n, 1n]>, Shape.clash(accepted))
    case 0n <> 1n <> 2n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_012(A, items, length),
        dims => length => product_012(dims, length), dims => coords => dl => cl => fit_012(dims, coords, dl, cl)}
    case 0n <> 1n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 0n <> 1n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(0n <> 1n <> (3n+p) <> Nil{}, 3n), Axis.unique(0n <> 1n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 0n <> 1n <> (3n+p) <> Nil{}), accepted)))))
    case 0n <> 2n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 2n, 0n]>, Shape.clash(accepted))
    case 0n <> 2n <> 1n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_021(A, items, length),
        dims => length => product_021(dims, length), dims => coords => dl => cl => fit_021(dims, coords, dl, cl)}
    case 0n <> 2n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [0n, 2n, 2n]>, Shape.clash(accepted))
    case 0n <> 2n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 0n <> 2n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(0n <> 2n <> (3n+p) <> Nil{}, 3n), Axis.unique(0n <> 2n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 0n <> 2n <> (3n+p) <> Nil{}), accepted)))))
    case 0n <> (3n+p) <> a0 <> Nil{}:
      Empty.absurd(Facts<3n, 0n <> (3n+p) <> a0 <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(a0 <> Nil{}, 3n), Arith.and_left(Axis.bounded(0n <> (3n+p) <> a0 <> Nil{}, 3n), Axis.unique(0n <> (3n+p) <> a0 <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 0n <> (3n+p) <> a0 <> Nil{}), accepted)))))
    case 1n <> 0n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 0n, 0n]>, Shape.clash(accepted))
    case 1n <> 0n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 0n, 1n]>, Shape.clash(accepted))
    case 1n <> 0n <> 2n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_102(A, items, length),
        dims => length => product_102(dims, length), dims => coords => dl => cl => fit_102(dims, coords, dl, cl)}
    case 1n <> 0n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 1n <> 0n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(1n <> 0n <> (3n+p) <> Nil{}, 3n), Axis.unique(1n <> 0n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 1n <> 0n <> (3n+p) <> Nil{}), accepted)))))
    case 1n <> 1n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 1n, 0n]>, Shape.clash(accepted))
    case 1n <> 1n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 1n, 1n]>, Shape.clash(accepted))
    case 1n <> 1n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 1n, 2n]>, Shape.clash(accepted))
    case 1n <> 1n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 1n <> 1n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(1n <> 1n <> (3n+p) <> Nil{}, 3n), Axis.unique(1n <> 1n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 1n <> 1n <> (3n+p) <> Nil{}), accepted)))))
    case 1n <> 2n <> 0n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_120(A, items, length),
        dims => length => product_120(dims, length), dims => coords => dl => cl => fit_120(dims, coords, dl, cl)}
    case 1n <> 2n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 2n, 1n]>, Shape.clash(accepted))
    case 1n <> 2n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [1n, 2n, 2n]>, Shape.clash(accepted))
    case 1n <> 2n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 1n <> 2n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(1n <> 2n <> (3n+p) <> Nil{}, 3n), Axis.unique(1n <> 2n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 1n <> 2n <> (3n+p) <> Nil{}), accepted)))))
    case 1n <> (3n+p) <> a0 <> Nil{}:
      Empty.absurd(Facts<3n, 1n <> (3n+p) <> a0 <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(a0 <> Nil{}, 3n), Arith.and_left(Axis.bounded(1n <> (3n+p) <> a0 <> Nil{}, 3n), Axis.unique(1n <> (3n+p) <> a0 <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 1n <> (3n+p) <> a0 <> Nil{}), accepted)))))
    case 2n <> 0n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 0n, 0n]>, Shape.clash(accepted))
    case 2n <> 0n <> 1n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_201(A, items, length),
        dims => length => product_201(dims, length), dims => coords => dl => cl => fit_201(dims, coords, dl, cl)}
    case 2n <> 0n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 0n, 2n]>, Shape.clash(accepted))
    case 2n <> 0n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 2n <> 0n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(2n <> 0n <> (3n+p) <> Nil{}, 3n), Axis.unique(2n <> 0n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 2n <> 0n <> (3n+p) <> Nil{}), accepted)))))
    case 2n <> 1n <> 0n <> Nil{}:
      Certified{{==}, {==}, {==}, A => items => length => lists_210(A, items, length),
        dims => length => product_210(dims, length), dims => coords => dl => cl => fit_210(dims, coords, dl, cl)}
    case 2n <> 1n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 1n, 1n]>, Shape.clash(accepted))
    case 2n <> 1n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 1n, 2n]>, Shape.clash(accepted))
    case 2n <> 1n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 2n <> 1n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(2n <> 1n <> (3n+p) <> Nil{}, 3n), Axis.unique(2n <> 1n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 2n <> 1n <> (3n+p) <> Nil{}), accepted)))))
    case 2n <> 2n <> 0n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 2n, 0n]>, Shape.clash(accepted))
    case 2n <> 2n <> 1n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 2n, 1n]>, Shape.clash(accepted))
    case 2n <> 2n <> 2n <> Nil{}:
      Empty.absurd(Facts<3n, [2n, 2n, 2n]>, Shape.clash(accepted))
    case 2n <> 2n <> (3n+p) <> Nil{}:
      Empty.absurd(Facts<3n, 2n <> 2n <> (3n+p) <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(Nil{}, 3n), Arith.and_left(Axis.bounded(2n <> 2n <> (3n+p) <> Nil{}, 3n), Axis.unique(2n <> 2n <> (3n+p) <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 2n <> 2n <> (3n+p) <> Nil{}), accepted)))))
    case 2n <> (3n+p) <> a0 <> Nil{}:
      Empty.absurd(Facts<3n, 2n <> (3n+p) <> a0 <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(a0 <> Nil{}, 3n), Arith.and_left(Axis.bounded(2n <> (3n+p) <> a0 <> Nil{}, 3n), Axis.unique(2n <> (3n+p) <> a0 <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, 2n <> (3n+p) <> a0 <> Nil{}), accepted)))))
    case (3n+p) <> a0 <> a1 <> Nil{}:
      Empty.absurd(Facts<3n, (3n+p) <> a0 <> a1 <> Nil{}>, Arith.lt_zero(p, Arith.and_left(Nat.is_lt(3n+p, 3n), Axis.bounded(a0 <> a1 <> Nil{}, 3n), Arith.and_left(Axis.bounded((3n+p) <> a0 <> a1 <> Nil{}, 3n), Axis.unique((3n+p) <> a0 <> a1 <> Nil{}), Equal.sym(Bool, True{}, Axis.valid(3n, (3n+p) <> a0 <> a1 <> Nil{}), accepted)))))
    case +a0 <> +a1 <> +a2 <> +a3 <> +tail:
      Empty.absurd(Facts<3n, a0 <> a1 <> a2 <> a3 <> tail>, Shape.clash(accepted))

Uses (31):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=and_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=lt_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=Facts
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_012
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_021
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_102
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_120
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_201
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=fit_210
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_012
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_021
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_102
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_120
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_201
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=lists_210
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_012
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_021
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_102
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_120
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_201
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=product_210
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=unique
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=valid