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, 6*	, ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	27, 7	⊢
	:
3	instantiation	30, 8, 9	,  ⊢
	: , : , :
4	reference	11	⊢
5	reference	12	⊢
6	instantiation	10, 11, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
8	instantiation	13, 17, 14, 37, 15*	⊢
	: , : , :
9	instantiation	16, 17, 18, 19, 20, 21, 22	,  ⊢
	: , : , : , :
10	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
11	instantiation	47, 43, 23	⊢
	: , : , :
12	instantiation	24, 25, 26	⊢
	: , :
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
14	instantiation	28	⊢
	: , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
18	instantiation	28	⊢
	: , :
19	instantiation	27, 37	⊢
	:
20	instantiation	28	⊢
	: , :
21	instantiation	30, 31, 29	⊢
	: , : , :
22	instantiation	30, 31, 32	⊢
	: , : , :
23	instantiation	47, 40, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
25	instantiation	47, 43, 34	⊢
	: , : , :
26	instantiation	47, 43, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	assumption		⊢
30	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
31	instantiation	36, 37, 38	⊢
	: , : , :
32	assumption		⊢
33	instantiation	47, 45, 39	⊢
	: , : , :
34	assumption		⊢
35	instantiation	47, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
38	instantiation	42, 43	⊢
	: , :
39	instantiation	47, 48, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	47, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	47, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements