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.logic.equality.four_chain_transitivity
2	instantiation	5, 6, 7, 28, 27	, ,  ⊢
	: , : , : , : , :
3	instantiation	8, 9, 10	,  ⊢
	: , : , :
4	instantiation	11	⊢
	:
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
6	instantiation	12, 20	⊢
	:
7	instantiation	13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	16, 17	,  ⊢
	: , :
10	instantiation	22, 18	,  ⊢
	: , : , :
11	axiom		⊢
	proveit.logic.equality.equals_reflexivity
12	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
13	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
14	instantiation	19, 20, 21	⊢
	: , : , :
15	assumption		⊢
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	22, 23	,  ⊢
	: , : , :
18	instantiation	24, 28, 27	,  ⊢
	: , :
19	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
21	instantiation	25, 31	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	26, 27, 28	,  ⊢
	: , :
24	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
25	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
26	theorem		⊢
	proveit.numbers.multiplication.commutation
27	instantiation	30, 31, 29	⊢
	: , : , :
28	instantiation	30, 31, 32	⊢
	: , : , :
29	assumption		⊢
30	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	assumption		⊢