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