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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	modus ponens	3, 4	, , , ,  ⊢
3	instantiation	5, 13, 14, 6	,  ⊢
	: , : , : , : , : , : , :
4	modus ponens	7, 8	, ,  ⊢
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
6	instantiation	9, 10, 11	,  ⊢
	: , : , :
7	instantiation	12, 13, 14	⊢
	: , : , : , : , : , :
8	generalization	15	, ,  ⊢
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	16, 28, 30	,  ⊢
	: , :
11	instantiation	17, 18, 19	,  ⊢
	: , :
12	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
14	instantiation	20, 32, 22, 23	⊢
	: , : , :
15	instantiation	21, 32, 22, 23, 24, 25, 26, 27	, , ,  ⊢
	: , : , : , :
16	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
17	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
18	instantiation	53, 29, 28	⊢
	: , : , :
19	instantiation	53, 29, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	instantiation	33	⊢
	: , : , :
23	instantiation	31, 32	⊢
	:
24	instantiation	33	⊢
	: , : , :
25	assumption		⊢
26	instantiation	34, 35	,  ⊢
	:
27	assumption		⊢
28	assumption		⊢
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	assumption		⊢
31	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
34	assumption		⊢
35	instantiation	36, 37, 38	⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
37	instantiation	53, 39, 51	⊢
	: , : , :
38	instantiation	40, 41	⊢
	: , :
39	instantiation	42, 49, 50	⊢
	: , :
40	theorem		⊢
	proveit.numbers.ordering.relax_less
41	instantiation	43, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
43	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
44	instantiation	46, 47	⊢
	:
45	instantiation	48, 49, 50, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
49	instantiation	53, 54, 52	⊢
	: , : , :
50	instantiation	53, 54, 55	⊢
	: , : , :
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat4