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