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	reference	27	⊢
2	modus ponens	3, 4	, , , ,  ⊢
3	instantiation	5, 33, 6, 11	⊢
	: , : , : , : , : , : , : , : , : , : , :
4	generalization	7	, , , ,  ⊢
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	instantiation	19, 8, 9	, , , , ,  ⊢
	: , : , :
8	instantiation	10, 11, 12, 13	, , , , ,  ⊢
	: , : , : , :
9	instantiation	14, 15, 16, 17	, , , , ,  ⊢
	: , : , : , :
10	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
11	instantiation	18, 42, 21, 34	⊢
	: , : , :
12	instantiation	19, 32, 39	,  ⊢
	: , : , :
13	instantiation	20, 42, 21, 34, 22, 35, 36, 37	, , ,  ⊢
	: , : , : , :
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	23, 24, 25	, , , , ,  ⊢
	: , : , :
16	instantiation	26	⊢
	:
17	instantiation	27, 28	,  ⊢
	: , :
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
19	theorem		⊢
	proveit.logic.equality.sub_left_side_into
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
21	instantiation	29	⊢
	: , : , :
22	instantiation	29	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	38, 30	,  ⊢
	: , : , :
25	instantiation	31, 32, 33, 34, 35, 36, 37	, , , , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
26	axiom		⊢
	proveit.logic.equality.equals_reflexivity
27	theorem		⊢
	proveit.logic.equality.equals_reversal
28	instantiation	38, 39	,  ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
30	instantiation	38, 39	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
32	instantiation	40, 51, 53	,  ⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	instantiation	41, 42	⊢
	:
35	assumption		⊢
36	instantiation	43, 44	,  ⊢
	:
37	assumption		⊢
38	axiom		⊢
	proveit.logic.equality.substitution
39	instantiation	45, 46, 47	,  ⊢
	: , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
41	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
43	assumption		⊢
44	instantiation	48, 49, 50	⊢
	:
45	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
46	instantiation	68, 52, 51	⊢
	: , : , :
47	instantiation	68, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
49	instantiation	68, 54, 66	⊢
	: , : , :
50	instantiation	55, 56	⊢
	: , :
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	assumption		⊢
54	instantiation	57, 64, 65	⊢
	: , :
55	theorem		⊢
	proveit.numbers.ordering.relax_less
56	instantiation	58, 59, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
58	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
59	instantiation	61, 62	⊢
	:
60	instantiation	63, 64, 65, 66	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
63	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
64	instantiation	68, 69, 67	⊢
	: , : , :
65	instantiation	68, 69, 70	⊢
	: , : , :
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat4