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	generalization	1	⊢
1	instantiation	40, 2, 3	,  ⊢
	: , : , :
2	instantiation	4, 5, 6	,  ⊢
	: , : , :
3	instantiation	32, 7, 8	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	9, 10	,  ⊢
	: , : , :
6	instantiation	11, 12, 13, 14	,  ⊢
	: , : , :
7	instantiation	35, 15	,  ⊢
	: , :
8	instantiation	16, 91, 77	,  ⊢
	: , :
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	17, 18, 89, 51, 19, 20, 52, 55, 56, 60, 61, 48, 54	,  ⊢
	: , : , : , : , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
13	instantiation	40, 21, 22	,  ⊢
	: , : , :
14	instantiation	40, 23, 24	⊢
	: , : , :
15	instantiation	25, 26	,  ⊢
	: , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket
17	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
19	instantiation	27	⊢
	: , : , : , :
20	instantiation	62	⊢
	: , :
21	instantiation	59, 43, 28	,  ⊢
	: , :
22	instantiation	32, 29, 30	,  ⊢
	: , : , :
23	instantiation	59, 43, 31	⊢
	: , :
24	instantiation	32, 33, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_eq
26	instantiation	35, 36	,  ⊢
	: , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
28	instantiation	40, 37, 38	,  ⊢
	: , : , :
29	instantiation	50, 94, 44, 51, 39, 52, 43, 60, 61, 48	,  ⊢
	: , : , : , : , : , :
30	instantiation	50, 51, 89, 44, 52, 45, 39, 55, 56, 60, 61, 48	,  ⊢
	: , : , : , : , : , :
31	instantiation	40, 41, 42	⊢
	: , : , :
32	axiom		⊢
	proveit.logic.equality.equals_transitivity
33	instantiation	50, 94, 44, 51, 46, 52, 43, 60, 61, 54	⊢
	: , : , : , : , : , :
34	instantiation	50, 51, 89, 44, 52, 45, 46, 55, 56, 60, 61, 54	⊢
	: , : , : , : , : , :
35	theorem		⊢
	proveit.logic.equality.equals_reversal
36	instantiation	47, 48, 54	,  ⊢
	: , :
37	instantiation	59, 49, 48	,  ⊢
	: , :
38	instantiation	50, 51, 89, 94, 52, 53, 60, 61, 48	,  ⊢
	: , : , : , : , : , :
39	instantiation	57	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	59, 49, 54	⊢
	: , :
42	instantiation	50, 51, 89, 94, 52, 53, 60, 61, 54	⊢
	: , : , : , : , : , :
43	instantiation	59, 55, 56	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
45	instantiation	62	⊢
	: , :
46	instantiation	57	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.commutation
48	instantiation	92, 67, 58	,  ⊢
	: , : , :
49	instantiation	59, 60, 61	⊢
	: , :
50	theorem		⊢
	proveit.numbers.multiplication.disassociation
51	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
52	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
53	instantiation	62	⊢
	: , :
54	instantiation	92, 67, 63	⊢
	: , : , :
55	instantiation	92, 67, 64	⊢
	: , : , :
56	instantiation	92, 67, 65	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
58	instantiation	92, 70, 66	,  ⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
61	instantiation	92, 67, 68	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	instantiation	92, 70, 69	⊢
	: , : , :
64	instantiation	92, 70, 71	⊢
	: , : , :
65	instantiation	92, 72, 73	⊢
	: , : , :
66	instantiation	92, 75, 74	,  ⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
68	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
69	instantiation	92, 75, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	92, 75, 85	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
74	instantiation	92, 76, 77	,  ⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	78, 79, 80	⊢
	: , :
77	assumption		⊢
78	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
79	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
80	instantiation	81, 82, 83	⊢
	: , :
81	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
82	instantiation	84, 85, 86	⊢
	: , :
83	instantiation	87, 88	⊢
	:
84	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
85	instantiation	92, 93, 89	⊢
	: , : , :
86	instantiation	92, 90, 91	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.negation.int_closure
88	instantiation	92, 93, 94	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
91	assumption		⊢
92	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
94	theorem		⊢
	proveit.numbers.numerals.decimals.nat1