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