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