Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	modus ponens	1, 2	, , , ,  ⊢
1	instantiation	3, 25, 4, 10	⊢
	: , : , : , : , : , : , : , : , : , : , :
2	generalization	5	, , , ,  ⊢
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	6, 7, 8	, , , , ,  ⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.sub_left_side_into
7	instantiation	9, 10, 13, 11	, , , , ,  ⊢
	: , : , : , :
8	instantiation	12, 13, 25, 27, 14, 29, 15, 32	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
9	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
10	instantiation	19, 21, 22, 27	⊢
	: , : , :
11	instantiation	16, 17, 18	, , , ,  ⊢
	: , : , :
12	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
13	assumption		⊢
14	instantiation	19, 50, 26, 27	⊢
	: , : , :
15	instantiation	20, 50, 26, 27, 28, 30, 31	, ,  ⊢
	: , : , : , :
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	20, 21, 22, 27, 23, 29, 30, 31, 32	, , , ,  ⊢
	: , : , : , :
18	instantiation	24, 25, 55, 26, 27, 28, 29, 30, 31, 32	, , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
22	instantiation	33	⊢
	: , : , : , :
23	instantiation	33	⊢
	: , : , : , :
24	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_association
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
26	instantiation	36	⊢
	: , :
27	instantiation	34, 35	⊢
	:
28	instantiation	36	⊢
	: , :
29	assumption		⊢
30	assumption		⊢
31	instantiation	37, 38	,  ⊢
	:
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
34	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	assumption		⊢
38	instantiation	39, 40, 41	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
40	instantiation	56, 42, 54	⊢
	: , : , :
41	instantiation	43, 44	⊢
	: , :
42	instantiation	45, 52, 53	⊢
	: , :
43	theorem		⊢
	proveit.numbers.ordering.relax_less
44	instantiation	46, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
46	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
47	instantiation	49, 50	⊢
	:
48	instantiation	51, 52, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
51	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
52	instantiation	56, 57, 55	⊢
	: , : , :
53	instantiation	56, 57, 58	⊢
	: , : , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat4