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	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	49, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	22, 23, 8, 9	⊢
	: , : , : , :
6	instantiation	49, 10	⊢
	: , : , :
7	instantiation	11, 82	⊢
	:
8	instantiation	12, 60, 13, 14	⊢
	: , :
9	instantiation	15, 23, 16, 17	⊢
	: , : , : , :
10	instantiation	49, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
12	theorem		⊢
	proveit.numbers.division.div_complex_closure
13	instantiation	19, 82	⊢
	:
14	instantiation	20, 29, 21	⊢
	: , :
15	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
16	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
17	instantiation	22, 23, 24, 25	⊢
	: , : , : , :
18	instantiation	49, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
20	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
21	instantiation	27, 28, 29	⊢
	: , :
22	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
23	instantiation	30, 43	⊢
	:
24	instantiation	81, 31, 32	⊢
	: , :
25	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
26	instantiation	49, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
28	instantiation	113, 35, 34	⊢
	: , : , :
29	instantiation	113, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
31	instantiation	113, 94, 37	⊢
	: , : , :
32	instantiation	51, 38, 39	⊢
	: , : , :
33	instantiation	49, 40	⊢
	: , : , :
34	instantiation	113, 42, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36	instantiation	113, 42, 43	⊢
	: , : , :
37	instantiation	113, 88, 44	⊢
	: , : , :
38	instantiation	73, 54, 45	⊢
	: , :
39	instantiation	46, 47, 48	⊢
	: , : , :
40	instantiation	49, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
45	instantiation	51, 52, 53	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	63, 115, 55, 64, 57, 65, 54, 74, 75, 67	⊢
	: , : , : , : , : , :
48	instantiation	63, 64, 105, 55, 65, 56, 57, 82, 68, 74, 75, 67	⊢
	: , : , : , : , : , :
49	axiom		⊢
	proveit.logic.equality.substitution
50	instantiation	58, 59, 60, 61*	⊢
	: , :
51	theorem		⊢
	proveit.logic.equality.sub_right_side_into
52	instantiation	73, 62, 67	⊢
	: , :
53	instantiation	63, 64, 105, 115, 65, 66, 74, 75, 67	⊢
	: , : , : , : , : , :
54	instantiation	73, 82, 68	⊢
	: , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
56	instantiation	76	⊢
	: , :
57	instantiation	69	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
59	instantiation	113, 94, 70	⊢
	: , : , :
60	instantiation	113, 94, 86	⊢
	: , : , :
61	instantiation	71, 72	⊢
	:
62	instantiation	73, 74, 75	⊢
	: , :
63	theorem		⊢
	proveit.numbers.multiplication.disassociation
64	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
65	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
66	instantiation	76	⊢
	: , :
67	instantiation	113, 94, 77	⊢
	: , : , :
68	instantiation	113, 94, 78	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
70	instantiation	113, 100, 79	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.double_negation
72	instantiation	113, 94, 80	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
75	instantiation	81, 82, 83	⊢
	: , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
77	instantiation	84, 85, 86, 87	⊢
	: , : , :
78	instantiation	113, 88, 89	⊢
	: , : , :
79	instantiation	113, 103, 90	⊢
	: , : , :
80	instantiation	91, 92, 110	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
82	instantiation	113, 94, 93	⊢
	: , : , :
83	instantiation	113, 94, 95	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
86	instantiation	113, 100, 96	⊢
	: , : , :
87	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
90	instantiation	111, 107	⊢
	:
91	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
92	instantiation	97, 98	⊢
	: , :
93	instantiation	113, 100, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
95	instantiation	113, 100, 101	⊢
	: , : , :
96	instantiation	113, 103, 112	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
99	instantiation	113, 103, 102	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
101	instantiation	113, 103, 104	⊢
	: , : , :
102	instantiation	113, 114, 105	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
104	instantiation	106, 107, 108	⊢
	: , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
106	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
107	instantiation	113, 109, 110	⊢
	: , : , :
108	instantiation	111, 112	⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	instantiation	113, 114, 115	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements