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	instantiation	1, 2	, ,  ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4	, ,  ⊢
	: , :
3	theorem		⊢
	proveit.logic.equality.equals_reversal
4	modus ponens	5, 6	, ,  ⊢
5	instantiation	7, 8, 9, 10	⊢
	: , : , : , : , : , : , : , : , : , :
6	generalization	11	, ,  ⊢
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	instantiation	12, 21, 14, 15	⊢
	: , : , :
11	instantiation	13, 21, 14, 15, 16, 17, 18, 19	, , ,  ⊢
	: , : , : , :
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
14	instantiation	22	⊢
	: , : , :
15	instantiation	20, 21	⊢
	:
16	instantiation	22	⊢
	: , : , :
17	assumption		⊢
18	instantiation	23, 24	,  ⊢
	:
19	assumption		⊢
20	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
23	assumption		⊢
24	instantiation	25, 26, 27	⊢
	:
25	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
26	instantiation	42, 28, 40	⊢
	: , : , :
27	instantiation	29, 30	⊢
	: , :
28	instantiation	31, 38, 39	⊢
	: , :
29	theorem		⊢
	proveit.numbers.ordering.relax_less
30	instantiation	32, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
32	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
33	instantiation	35, 36	⊢
	:
34	instantiation	37, 38, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
38	instantiation	42, 43, 41	⊢
	: , : , :
39	instantiation	42, 43, 44	⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4