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, 3	, , , ,  ⊢
	: , : , :
1	reference	8	⊢
2	instantiation	8, 4, 5	, , , ,  ⊢
	: , : , :
3	modus ponens	6, 7	, , , ,  ⊢
4	instantiation	8, 9, 10	, , ,  ⊢
	: , : , :
5	instantiation	18, 11	, ,  ⊢
	: , : , :
6	instantiation	12, 40, 13, 42, 14, 24, 44	⊢
	: , : , : , : , : , : , : , :
7	instantiation	33, 34, 21, 45, 23, 15, 47, 16	, , , ,  ⊢
	: , : , : , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	18, 17	, ,  ⊢
	: , : , :
10	instantiation	18, 19	, ,  ⊢
	: , : , :
11	instantiation	29, 20	, ,  ⊢
	: , :
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_factorization_from_add
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
14	instantiation	31, 34, 21, 45, 23	⊢
	: , : , :
15	instantiation	52	⊢
	: , :
16	instantiation	22, 51, 23, 24, 25, 26, 27	, , ,  ⊢
	: , : , : , :
17	instantiation	29, 28	, ,  ⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.substitution
19	instantiation	29, 30	, ,  ⊢
	: , :
20	instantiation	39, 40, 41, 42, 43, 44, 45, 35, 47, 48, 36	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
21	instantiation	52	⊢
	: , :
22	theorem		⊢
	proveit.linear_algebra.addition.closure
23	instantiation	31, 34, 43, 45	⊢
	: , : , :
24	instantiation	32	⊢
	: , : , :
25	instantiation	33, 34, 43, 45, 37, 48, 38	,  ⊢
	: , : , : , :
26	instantiation	33, 34, 43, 45, 46, 48, 49	,  ⊢
	: , : , : , :
27	instantiation	33, 34, 43, 45, 35, 48, 36	,  ⊢
	: , : , : , :
28	instantiation	39, 40, 41, 42, 43, 44, 45, 37, 47, 48, 38	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
29	theorem		⊢
	proveit.logic.equality.equals_reversal
30	instantiation	39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
31	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
33	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
35	instantiation	52	⊢
	: , :
36	assumption		⊢
37	instantiation	52	⊢
	: , :
38	assumption		⊢
39	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
43	instantiation	52	⊢
	: , :
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	50, 51	⊢
	:
46	instantiation	52	⊢
	: , :
47	assumption		⊢
48	assumption		⊢
49	assumption		⊢
50	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq