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	reference	13	⊢
2	instantiation	32, 5	, ,  ⊢
	: , : , :
3	instantiation	32, 6	, ,  ⊢
	: , : , :
4	instantiation	7, 35, 8, 9, 41, 10, 11	, , , ,  ⊢
	: , : , : , : , :
5	instantiation	25, 12	, ,  ⊢
	: , :
6	instantiation	13, 14, 15, 16	, ,  ⊢
	: , : , : , :
7	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.factorization_from_vectors
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
9	instantiation	17	⊢
	: , :
10	instantiation	44, 45, 18	,  ⊢
	: , : , :
11	instantiation	27, 35, 42, 36	,  ⊢
	: , : , : , :
12	instantiation	34, 35, 19, 41, 30, 20*	, ,  ⊢
	: , : , : , : , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	21	⊢
	:
15	instantiation	22, 23, 24	,  ⊢
	: , : , :
16	instantiation	25, 26	, ,  ⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	instantiation	27, 28, 38, 29	,  ⊢
	: , : , : , :
19	instantiation	44, 45, 29	⊢
	: , : , :
20	instantiation	40, 41, 30	,  ⊢
	: , :
21	axiom		⊢
	proveit.logic.equality.equals_reflexivity
22	theorem		⊢
	proveit.logic.equality.sub_left_side_into
23	instantiation	32, 31	,  ⊢
	: , : , :
24	instantiation	32, 33	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	34, 35, 36, 41, 42	, ,  ⊢
	: , : , : , : , :
27	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
28	instantiation	37, 50	⊢
	:
29	assumption		⊢
30	instantiation	47, 53, 38	⊢
	: , : , :
31	instantiation	39, 42, 41	,  ⊢
	: , :
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	40, 41, 42	,  ⊢
	: , :
34	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
35	instantiation	43, 50	⊢
	:
36	instantiation	44, 45, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.multiplication.commutation
40	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
41	assumption		⊢
42	instantiation	47, 53, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
44	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
45	instantiation	49, 50, 51	⊢
	: , : , :
46	assumption		⊢
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	assumption		⊢
49	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
51	instantiation	52, 53	⊢
	: , :
52	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements