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*	, ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	25, 6	⊢
	:
3	instantiation	28, 7, 8	,  ⊢
	: , : , :
4	reference	32	⊢
5	instantiation	9, 32, 10*	⊢
	: , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
7	instantiation	11, 15, 12, 34, 13*	⊢
	: , : , :
8	instantiation	14, 15, 16, 17, 18, 19, 20	,  ⊢
	: , : , : , :
9	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
10	instantiation	21, 32, 22, 23*, 24*	⊢
	: , : , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
12	instantiation	26	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
16	instantiation	26	⊢
	: , :
17	instantiation	25, 34	⊢
	:
18	instantiation	26	⊢
	: , :
19	instantiation	28, 29, 27	⊢
	: , : , :
20	instantiation	28, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
23	instantiation	31, 32	⊢
	:
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
25	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	assumption		⊢
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	33, 34, 35	⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
32	instantiation	36, 39, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	instantiation	38, 39	⊢
	: , :
36	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
37	assumption		⊢
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements