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	modus ponens	1, 2	⊢
1	instantiation	3, 88, 4, 47, 10, 48	⊢
	: , : , : , : , : , : , : , : , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	6, 7, 8	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.sub_left_side_into
7	instantiation	9, 10, 13, 11	,  ⊢
	: , : , : , :
8	instantiation	12, 13, 88, 47, 48, 17, 18, 20, 21	,  ⊢
	: , : , : , : , : , : , : , : , : , :
9	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
10	instantiation	14, 25, 16, 17, 18	⊢
	: , : , :
11	instantiation	15, 25, 16, 17, 18, 19, 20, 21	,  ⊢
	: , : , : , :
12	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
13	instantiation	22, 23, 24	,  ⊢
	: , :
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
15	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
16	instantiation	57	⊢
	: , :
17	instantiation	26, 25	⊢
	:
18	instantiation	26, 27	⊢
	:
19	instantiation	57	⊢
	: , :
20	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
21	instantiation	28, 85, 71	,  ⊢
	: , :
22	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
23	instantiation	86, 61, 29	⊢
	: , : , :
24	instantiation	38, 30, 31	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
26	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
27	instantiation	32, 83, 80	⊢
	: , :
28	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
29	instantiation	86, 66, 33	⊢
	: , : , :
30	instantiation	54, 41, 34	,  ⊢
	: , :
31	instantiation	35, 36, 37	,  ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
34	instantiation	38, 39, 40	,  ⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	46, 88, 42, 47, 44, 48, 41, 55, 56, 50	,  ⊢
	: , : , : , : , : , :
37	instantiation	46, 47, 83, 42, 48, 43, 44, 51, 52, 55, 56, 50	,  ⊢
	: , : , : , : , : , :
38	theorem		⊢
	proveit.logic.equality.sub_right_side_into
39	instantiation	54, 45, 50	,  ⊢
	: , :
40	instantiation	46, 47, 83, 88, 48, 49, 55, 56, 50	,  ⊢
	: , : , : , : , : , :
41	instantiation	54, 51, 52	⊢
	: , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
43	instantiation	57	⊢
	: , :
44	instantiation	53	⊢
	: , : , :
45	instantiation	54, 55, 56	⊢
	: , :
46	theorem		⊢
	proveit.numbers.multiplication.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	57	⊢
	: , :
50	instantiation	86, 61, 58	,  ⊢
	: , : , :
51	instantiation	86, 61, 59	⊢
	: , : , :
52	instantiation	86, 61, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
54	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
56	instantiation	86, 61, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	instantiation	86, 64, 63	,  ⊢
	: , : , :
59	instantiation	86, 64, 65	⊢
	: , : , :
60	instantiation	86, 66, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
63	instantiation	86, 69, 68	,  ⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	86, 69, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
68	instantiation	86, 70, 71	,  ⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	72, 73, 74	⊢
	: , :
71	assumption		⊢
72	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
73	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
74	instantiation	75, 76, 77	⊢
	: , :
75	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
76	instantiation	78, 79, 80	⊢
	: , :
77	instantiation	81, 82	⊢
	:
78	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
79	instantiation	86, 87, 83	⊢
	: , : , :
80	instantiation	86, 84, 85	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.negation.int_closure
82	instantiation	86, 87, 88	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
85	assumption		⊢
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1