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	, , ,  ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	35, 4	, ,  ⊢
	: , : , :
3	instantiation	5, 19, 6, 7, 41, 8, 9	, , ,  ⊢
	: , : , : , : , :
4	instantiation	29, 10	, ,  ⊢
	: , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.factorization_from_vectors
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
7	instantiation	11	⊢
	: , :
8	instantiation	26, 27, 12	⊢
	: , : , :
9	instantiation	13, 19, 40, 20	,  ⊢
	: , : , : , :
10	instantiation	14, 15, 16, 17	, ,  ⊢
	: , : , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	assumption		⊢
13	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	18, 19, 20, 41, 40	, ,  ⊢
	: , : , : , : , :
16	instantiation	21, 22, 23	,  ⊢
	: , : , :
17	instantiation	24	⊢
	:
18	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
19	instantiation	25, 33	⊢
	:
20	instantiation	26, 27, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.sub_left_side_into
22	instantiation	29, 30	,  ⊢
	: , :
23	instantiation	35, 31	,  ⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
26	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
27	instantiation	32, 33, 34	⊢
	: , : , :
28	assumption		⊢
29	theorem		⊢
	proveit.logic.equality.equals_reversal
30	instantiation	35, 36	,  ⊢
	: , : , :
31	instantiation	37, 41, 40	,  ⊢
	: , :
32	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
34	instantiation	38, 44	⊢
	: , :
35	axiom		⊢
	proveit.logic.equality.substitution
36	instantiation	39, 40, 41	,  ⊢
	: , :
37	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.multiplication.commutation
40	instantiation	43, 44, 42	⊢
	: , : , :
41	instantiation	43, 44, 45	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	assumption		⊢