AxisAlgebra.fit_210: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend as AxisAlgebra
Lines 723-744 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=723&end_line=744

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

def fit_210(+dims: List<&2, Nat>, +coords: List<&2, Nat>, dl: {List.length(&2, Nat, dims) == 3n : Nat}, cl: {List.length(&2, Nat, coords) == 3n : Nat}) -> {Shape.fit(Axis.order(Nat, dims, [2n, 1n, 0n]), Axis.order(Nat, coords, [2n, 1n, 0n])) == Shape.fit(dims, coords) : Bool}:
  match dims:
    case Nil{}:
      Empty.absurd({Shape.fit(Axis.order(Nat, Nil{}, [2n, 1n, 0n]), Axis.order(Nat, coords, [2n, 1n, 0n])) == Shape.fit(Nil{}, coords) : Bool}, nat_clash(0n, 3n, dl, {==}))
    case +d0 <> Nil{}:
      Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, coords, [2n, 1n, 0n])) == Shape.fit(d0 <> Nil{}, coords) : Bool}, nat_clash(1n, 3n, dl, {==}))
    case +d0 <> +d1 <> Nil{}:
      Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, coords, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> Nil{}, coords) : Bool}, nat_clash(2n, 3n, dl, {==}))
    case +d0 <> +d1 <> +d2 <> Nil{}:
      match coords:
        case Nil{}:
          Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> d2 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, Nil{}, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> d2 <> Nil{}, Nil{}) : Bool}, nat_clash(0n, 3n, cl, {==}))
        case +c0 <> Nil{}:
          Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> d2 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, c0 <> Nil{}, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> d2 <> Nil{}, c0 <> Nil{}) : Bool}, nat_clash(1n, 3n, cl, {==}))
        case +c0 <> +c1 <> Nil{}:
          Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> d2 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, c0 <> c1 <> Nil{}, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> d2 <> Nil{}, c0 <> c1 <> Nil{}) : Bool}, nat_clash(2n, 3n, cl, {==}))
        case +c0 <> +c1 <> +c2 <> Nil{}:
          Equal.trans(Bool, Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c0, d0), True{}))), Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), True{}))), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c2, d2), True{}))), Equal.cong(Bool, Bool, value => Bool.and(Nat.is_lt(c2, d2), value), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c0, d0), True{})), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), True{})), and_swap(Nat.is_lt(c1, d1), Nat.is_lt(c0, d0), True{})), Equal.trans(Bool, Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), True{}))), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c1, d1), True{}))), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c2, d2), True{}))), and_swap(Nat.is_lt(c2, d2), Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), True{})), Equal.trans(Bool, Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c1, d1), True{}))), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c2, d2), True{}))), Bool.and(Nat.is_lt(c0, d0), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c2, d2), True{}))), Equal.cong(Bool, Bool, value => Bool.and(Nat.is_lt(c0, d0), value), Bool.and(Nat.is_lt(c2, d2), Bool.and(Nat.is_lt(c1, d1), True{})), Bool.and(Nat.is_lt(c1, d1), Bool.and(Nat.is_lt(c2, d2), True{})), and_swap(Nat.is_lt(c2, d2), Nat.is_lt(c1, d1), True{})), {==})))
        case +c0 <> +c1 <> +c2 <> +c3 <> +ct:
          Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> d2 <> Nil{}, [2n, 1n, 0n]), Axis.order(Nat, c0 <> c1 <> c2 <> c3 <> ct, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> d2 <> Nil{}, c0 <> c1 <> c2 <> c3 <> ct) : Bool}, nat_clash(4n+List.length(&2, Nat, ct), 3n, cl, {==}))
    case +d0 <> +d1 <> +d2 <> +d3 <> +dt:
      Empty.absurd({Shape.fit(Axis.order(Nat, d0 <> d1 <> d2 <> d3 <> dt, [2n, 1n, 0n]), Axis.order(Nat, coords, [2n, 1n, 0n])) == Shape.fit(d0 <> d1 <> d2 <> d3 <> dt, coords) : Bool}, nat_clash(4n+List.length(&2, Nat, dt), 3n, dl, {==}))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  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=fit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=and_swap
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=nat_clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=order