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, 31, 4, 9	⊢
	: , : , : , : , : , : , : , : , : , : , :
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	17, 6, 7	, , , , ,  ⊢
	: , : , :
6	instantiation	8, 9, 10, 11	, , , , ,  ⊢
	: , : , : , :
7	instantiation	12, 13, 14, 15	, , , , ,  ⊢
	: , : , : , :
8	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
9	instantiation	16, 40, 19, 32	⊢
	: , : , :
10	instantiation	17, 30, 37	,  ⊢
	: , : , :
11	instantiation	18, 40, 19, 32, 20, 33, 34, 35	, , ,  ⊢
	: , : , : , :
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	21, 22, 23	, , , , ,  ⊢
	: , : , :
14	instantiation	24	⊢
	:
15	instantiation	25, 26	,  ⊢
	: , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.logic.equality.sub_left_side_into
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
19	instantiation	27	⊢
	: , : , :
20	instantiation	27	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	36, 28	,  ⊢
	: , : , :
23	instantiation	29, 30, 31, 32, 33, 34, 35	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	36, 37	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	instantiation	36, 37	,  ⊢
	: , : , :
29	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
30	instantiation	38, 49, 51	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
32	instantiation	39, 40	⊢
	:
33	assumption		⊢
34	instantiation	41, 42	,  ⊢
	:
35	assumption		⊢
36	axiom		⊢
	proveit.logic.equality.substitution
37	instantiation	43, 44, 45	,  ⊢
	: , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
39	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
41	assumption		⊢
42	instantiation	46, 47, 48	⊢
	:
43	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
44	instantiation	66, 50, 49	⊢
	: , : , :
45	instantiation	66, 50, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
47	instantiation	66, 52, 64	⊢
	: , : , :
48	instantiation	53, 54	⊢
	: , :
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	assumption		⊢
52	instantiation	55, 62, 63	⊢
	: , :
53	theorem		⊢
	proveit.numbers.ordering.relax_less
54	instantiation	56, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
57	instantiation	59, 60	⊢
	:
58	instantiation	61, 62, 63, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
61	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
62	instantiation	66, 67, 65	⊢
	: , : , :
63	instantiation	66, 67, 68	⊢
	: , : , :
64	assumption		⊢
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat4