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, 3, 4	, ,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
2	instantiation	5, 9, 10, 11	⊢
	: , : , :
3	instantiation	6, 16, 7	⊢
	: , :
4	instantiation	8, 9, 10, 11, 12, 13, 14	,  ⊢
	: , : , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
6	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
7	instantiation	15, 16, 17	⊢
	: , :
8	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
10	instantiation	20	⊢
	: , :
11	instantiation	18, 19	⊢
	:
12	instantiation	20	⊢
	: , :
13	assumption		⊢
14	assumption		⊢
15	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
16	instantiation	34, 22, 21	⊢
	: , : , :
17	instantiation	34, 22, 23	⊢
	: , : , :
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	instantiation	34, 25, 24	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
23	instantiation	34, 25, 26	⊢
	: , : , :
24	instantiation	34, 27, 28	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
26	instantiation	34, 35, 29	⊢
	: , : , :
27	instantiation	30, 31, 32	⊢
	: , :
28	assumption		⊢
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
31	instantiation	34, 35, 33	⊢
	: , : , :
32	instantiation	34, 35, 36	⊢
	: , : , :
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