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, 8, 9, 10	⊢
	: , : , :
3	instantiation	41, 33, 6	⊢
	: , : , :
4	instantiation	7, 8, 9, 10, 11, 12, 13	,  ⊢
	: , : , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
6	instantiation	14, 15, 16	⊢
	: , :
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
8	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
9	instantiation	18	⊢
	: , :
10	instantiation	17, 27	⊢
	:
11	instantiation	18	⊢
	: , :
12	instantiation	20, 21, 19	⊢
	: , : , :
13	instantiation	20, 21, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
15	instantiation	41, 24, 23	⊢
	: , : , :
16	instantiation	41, 24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	assumption		⊢
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	26, 27, 28	⊢
	: , : , :
22	assumption		⊢
23	instantiation	41, 30, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
25	instantiation	41, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
28	instantiation	32, 33	⊢
	: , :
29	instantiation	41, 34, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	41, 42, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	37, 38, 39	⊢
	: , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
38	instantiation	41, 42, 40	⊢
	: , : , :
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4