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, 10, 11, 6	⊢
	: , : , : , : , : , : , :
4	modus ponens	7, 8	,  ⊢
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
6	assumption		⊢
7	instantiation	9, 10, 11	⊢
	: , : , : , : , : , :
8	generalization	12	,  ⊢
9	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
11	instantiation	13, 36, 15, 16	⊢
	: , : , :
12	instantiation	14, 36, 15, 16, 17, 18, 19	, ,  ⊢
	: , : , : , :
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
15	instantiation	22	⊢
	: , :
16	instantiation	20, 21	⊢
	:
17	instantiation	22	⊢
	: , :
18	assumption		⊢
19	instantiation	23, 24	,  ⊢
	:
20	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	assumption		⊢
24	instantiation	25, 26, 27	⊢
	:
25	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
26	instantiation	42, 28, 40	⊢
	: , : , :
27	instantiation	29, 30	⊢
	: , :
28	instantiation	31, 38, 39	⊢
	: , :
29	theorem		⊢
	proveit.numbers.ordering.relax_less
30	instantiation	32, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
32	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
33	instantiation	35, 36	⊢
	:
34	instantiation	37, 38, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
38	instantiation	42, 43, 41	⊢
	: , : , :
39	instantiation	42, 43, 44	⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4