def product_3102

bendtorch-core@0.1.0.0 · src/tensor/axis_algebra.bend:1901

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

1901def product_3102(+dims: List<&2, Nat>, length: {List.length(&2, Nat, dims) == 4n : Nat}) -> {Shape.numel(Axis.order(Nat, dims, [3n, 1n, 0n, 2n])) == Shape.numel(dims) : Nat}:
1902  match dims:
1903    case Nil{}:
1904      Empty.absurd({Shape.numel(Axis.order(Nat, Nil{}, [3n, 1n, 0n, 2n])) == Shape.numel(Nil{}) : Nat}, nat_clash(0n, 4n, length, {==}))
1905    case +x0 <> Nil{}:
1906      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> Nil{}, [3n, 1n, 0n, 2n])) == Shape.numel(x0 <> Nil{}) : Nat}, nat_clash(1n, 4n, length, {==}))
1907    case +x0 <> +x1 <> Nil{}:
1908      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> Nil{}, [3n, 1n, 0n, 2n])) == Shape.numel(x0 <> x1 <> Nil{}) : Nat}, nat_clash(2n, 4n, length, {==}))
1909    case +x0 <> +x1 <> +x2 <> Nil{}:
1910      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> Nil{}, [3n, 1n, 0n, 2n])) == Shape.numel(x0 <> x1 <> x2 <> Nil{}) : Nat}, nat_clash(3n, 4n, length, {==}))
1911    case +x0 <> +x1 <> +x2 <> +x3 <> Nil{}:
1912      Equal.trans(Nat, Nat.mul(x3, Nat.mul(x1, Nat.mul(x0, Nat.mul(x2, 1n)))), Nat.mul(x3, Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Equal.cong(Nat, Nat, value => Nat.mul(x3, value), Nat.mul(x1, Nat.mul(x0, Nat.mul(x2, 1n))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n))), mul_swap(x1, x0, Nat.mul(x2, 1n))), Equal.trans(Nat, Nat.mul(x3, Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x3, Nat.mul(x1, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), mul_swap(x3, x0, Nat.mul(x1, Nat.mul(x2, 1n))), Equal.trans(Nat, Nat.mul(x0, Nat.mul(x3, Nat.mul(x1, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x3, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Equal.cong(Nat, Nat, value => Nat.mul(x0, value), Nat.mul(x3, Nat.mul(x1, Nat.mul(x2, 1n))), Nat.mul(x1, Nat.mul(x3, Nat.mul(x2, 1n))), mul_swap(x3, x1, Nat.mul(x2, 1n))), Equal.trans(Nat, Nat.mul(x0, Nat.mul(x1, Nat.mul(x3, Nat.mul(x2, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Equal.cong(Nat, Nat, value => Nat.mul(x0, Nat.mul(x1, value)), Nat.mul(x3, Nat.mul(x2, 1n)), Nat.mul(x2, Nat.mul(x3, 1n)), mul_swap(x3, x2, 1n)), {==}))))
1913    case +x0 <> +x1 <> +x2 <> +x3 <> +x4 <> +tail:
1914      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> x3 <> x4 <> tail, [3n, 1n, 0n, 2n])) == Shape.numel(x0 <> x1 <> x2 <> x3 <> x4 <> tail) : Nat}, nat_clash(5n+List.length(&2, Nat, tail), 4n, length, {==}))