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	4, 5	, ,  ⊢
	: , : , :
3	instantiation	6, 7, 8, 42, 9*	, ,  ⊢
	: , : , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	10, 47, 11, 12, 13, 14, 37, 40	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
6	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
7	instantiation	35, 15	⊢
	:
8	instantiation	38, 16, 17	,  ⊢
	: , : , :
9	instantiation	18, 42, 19*	⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	20, 44	⊢
	:
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
16	instantiation	21, 25, 22, 44, 23*	⊢
	: , : , :
17	instantiation	24, 25, 26, 27, 28, 29, 30	,  ⊢
	: , : , : , :
18	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
19	instantiation	31, 42, 32, 33*, 34*	⊢
	: , : , :
20	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
22	instantiation	36	⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
24	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
26	instantiation	36	⊢
	: , :
27	instantiation	35, 44	⊢
	:
28	instantiation	36	⊢
	: , :
29	instantiation	38, 39, 37	⊢
	: , : , :
30	instantiation	38, 39, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
33	instantiation	41, 42	⊢
	:
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
35	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	assumption		⊢
38	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
39	instantiation	43, 44, 45	⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
42	instantiation	46, 49, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	instantiation	48, 49	⊢
	: , :
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	assumption		⊢
48	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
*equality replacement requirements