def product_3201

bendtorch-core@0.1.0.0 · src/tensor/axis_algebra.bend:2015

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

2015def product_3201(+dims: List<&2, Nat>, length: {List.length(&2, Nat, dims) == 4n : Nat}) -> {Shape.numel(Axis.order(Nat, dims, [3n, 2n, 0n, 1n])) == Shape.numel(dims) : Nat}:
2016  match dims:
2017    case Nil{}:
2018      Empty.absurd({Shape.numel(Axis.order(Nat, Nil{}, [3n, 2n, 0n, 1n])) == Shape.numel(Nil{}) : Nat}, nat_clash(0n, 4n, length, {==}))
2019    case +x0 <> Nil{}:
2020      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> Nil{}, [3n, 2n, 0n, 1n])) == Shape.numel(x0 <> Nil{}) : Nat}, nat_clash(1n, 4n, length, {==}))
2021    case +x0 <> +x1 <> Nil{}:
2022      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> Nil{}, [3n, 2n, 0n, 1n])) == Shape.numel(x0 <> x1 <> Nil{}) : Nat}, nat_clash(2n, 4n, length, {==}))
2023    case +x0 <> +x1 <> +x2 <> Nil{}:
2024      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> Nil{}, [3n, 2n, 0n, 1n])) == Shape.numel(x0 <> x1 <> x2 <> Nil{}) : Nat}, nat_clash(3n, 4n, length, {==}))
2025    case +x0 <> +x1 <> +x2 <> +x3 <> Nil{}:
2026      Equal.trans(Nat, Nat.mul(x3, Nat.mul(x2, Nat.mul(x0, Nat.mul(x1, 1n)))), Nat.mul(x3, Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, 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(x2, Nat.mul(x0, Nat.mul(x1, 1n))), Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, 1n))), mul_swap(x2, x0, Nat.mul(x1, 1n))), Equal.trans(Nat, Nat.mul(x3, Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, 1n)))), Nat.mul(x0, Nat.mul(x3, Nat.mul(x2, Nat.mul(x1, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), mul_swap(x3, x0, Nat.mul(x2, Nat.mul(x1, 1n))), Equal.trans(Nat, Nat.mul(x0, Nat.mul(x3, Nat.mul(x2, Nat.mul(x1, 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)))), Equal.cong(Nat, Nat, value => Nat.mul(x0, Nat.mul(x3, value)), Nat.mul(x2, Nat.mul(x1, 1n)), Nat.mul(x1, Nat.mul(x2, 1n)), mul_swap(x2, x1, 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)), {==})))))
2027    case +x0 <> +x1 <> +x2 <> +x3 <> +x4 <> +tail:
2028      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> x3 <> x4 <> tail, [3n, 2n, 0n, 1n])) == Shape.numel(x0 <> x1 <> x2 <> x3 <> x4 <> tail) : Nat}, nat_clash(5n+List.length(&2, Nat, tail), 4n, length, {==}))