def product_201

bendtorch-core@0.1.0.0 · src/tensor/axis_algebra.bend:661

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

661def product_201(+dims: List<&2, Nat>, length: {List.length(&2, Nat, dims) == 3n : Nat}) -> {Shape.numel(Axis.order(Nat, dims, [2n, 0n, 1n])) == Shape.numel(dims) : Nat}:
662  match dims:
663    case Nil{}:
664      Empty.absurd({Shape.numel(Axis.order(Nat, Nil{}, [2n, 0n, 1n])) == Shape.numel(Nil{}) : Nat}, nat_clash(0n, 3n, length, {==}))
665    case +x0 <> Nil{}:
666      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> Nil{}, [2n, 0n, 1n])) == Shape.numel(x0 <> Nil{}) : Nat}, nat_clash(1n, 3n, length, {==}))
667    case +x0 <> +x1 <> Nil{}:
668      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> Nil{}, [2n, 0n, 1n])) == Shape.numel(x0 <> x1 <> Nil{}) : Nat}, nat_clash(2n, 3n, length, {==}))
669    case +x0 <> +x1 <> +x2 <> Nil{}:
670      Equal.trans(Nat, Nat.mul(x2, Nat.mul(x0, Nat.mul(x1, 1n))), Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, 1n))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n))), mul_swap(x2, x0, Nat.mul(x1, 1n)), Equal.trans(Nat, Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, 1n))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, 1n))), Equal.cong(Nat, Nat, value => Nat.mul(x0, value), Nat.mul(x2, Nat.mul(x1, 1n)), Nat.mul(x1, Nat.mul(x2, 1n)), mul_swap(x2, x1, 1n)), {==}))
671    case +x0 <> +x1 <> +x2 <> +x3 <> +tail:
672      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> x3 <> tail, [2n, 0n, 1n])) == Shape.numel(x0 <> x1 <> x2 <> x3 <> tail) : Nat}, nat_clash(4n+List.length(&2, Nat, tail), 3n, length, {==}))