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