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, 14	⊢
	:
12	instantiation	15, 16	,  ⊢
	:
13	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
15	assumption		⊢
16	instantiation	17, 18, 19	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
18	instantiation	34, 20, 32	⊢
	: , : , :
19	instantiation	21, 22	⊢
	: , :
20	instantiation	23, 30, 31	⊢
	: , :
21	theorem		⊢
	proveit.numbers.ordering.relax_less
22	instantiation	24, 25, 26	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
24	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
25	instantiation	27, 28	⊢
	:
26	instantiation	29, 30, 31, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
29	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
30	instantiation	34, 35, 33	⊢
	: , : , :
31	instantiation	34, 35, 36	⊢
	: , : , :
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
35	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat4