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*, 6*	,  ⊢
	: , : , : , :
1	reference	21	⊢
2	reference	27	⊢
3	instantiation	154, 134, 7	⊢
	: , : , :
4	instantiation	8, 18, 28, 12	,  ⊢
	: , : , : , :
5	instantiation	9, 10	⊢
	:
6	instantiation	11, 18, 28, 12, 13, 14*	,  ⊢
	: , : , : , :
7	instantiation	154, 127, 24	⊢
	: , : , :
8	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
9	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.linear_algebra.addition.norm_of_sum_of_orthogonal_pair
12	instantiation	17, 18, 49, 29	,  ⊢
	: , : , : , :
13	instantiation	89, 19, 20	,  ⊢
	: , : , :
14	instantiation	21, 27, 49, 29, 22*	,  ⊢
	: , : , : , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
16	instantiation	154, 23, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
18	instantiation	25, 88	⊢
	:
19	instantiation	26, 27, 49, 28, 29	,  ⊢
	: , : , : , : , :
20	instantiation	84, 30, 31	,  ⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.inner_products.scaled_norm
22	instantiation	84, 32, 33	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
24	instantiation	34, 35, 58, 36	⊢
	: , :
25	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
26	theorem		⊢
	proveit.linear_algebra.inner_products.inner_prod_scalar_mult_right
27	instantiation	37, 88	⊢
	:
28	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
29	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
30	instantiation	74, 38	⊢
	: , : , :
31	instantiation	39, 49, 40, 41*	,  ⊢
	: , :
32	instantiation	74, 42	,  ⊢
	: , : , :
33	instantiation	43, 44	⊢
	:
34	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
35	instantiation	154, 77, 45	⊢
	: , : , :
36	instantiation	46, 47	⊢
	:
37	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_inner_prod_space
38	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_and_one_have_zero_inner_prod
39	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
41	instantiation	48, 49	,  ⊢
	:
42	instantiation	50, 51, 52*	,  ⊢
	:
43	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
44	instantiation	53, 54, 55	⊢
	: , : , :
45	instantiation	154, 87, 56	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
47	instantiation	154, 57, 58	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
49	instantiation	124, 59, 60	,  ⊢
	: , :
50	theorem		⊢
	proveit.numbers.absolute_value.complex_unit_length
51	instantiation	89, 61, 62	,  ⊢
	: , : , :
52	instantiation	63, 64	,  ⊢
	: , :
53	theorem		⊢
	proveit.logic.equality.sub_left_side_into
54	instantiation	154, 134, 65	⊢
	: , : , :
55	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_norm
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
58	instantiation	66, 67	⊢
	:
59	instantiation	154, 134, 68	⊢
	: , : , :
60	instantiation	89, 69, 70	,  ⊢
	: , : , :
61	instantiation	120, 110, 71	,  ⊢
	: , :
62	instantiation	84, 72, 73	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.logic.equality.equals_reversal
64	instantiation	74, 75	,  ⊢
	: , : , :
65	instantiation	154, 137, 76	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
67	instantiation	154, 77, 78	⊢
	: , : , :
68	instantiation	154, 127, 79	⊢
	: , : , :
69	instantiation	115, 92, 80	,  ⊢
	: , :
70	instantiation	84, 81, 82	,  ⊢
	: , : , :
71	instantiation	120, 83, 119	,  ⊢
	: , :
72	instantiation	105, 153, 139, 106, 99, 107, 92, 117, 109	,  ⊢
	: , : , : , : , : , :
73	instantiation	105, 106, 139, 107, 98, 99, 125, 103, 117, 109	,  ⊢
	: , : , : , : , : , :
74	axiom		⊢
	proveit.logic.equality.substitution
75	instantiation	84, 85, 86	,  ⊢
	: , : , :
76	instantiation	154, 140, 149	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
78	instantiation	154, 87, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
80	instantiation	89, 90, 91	,  ⊢
	: , : , :
81	instantiation	105, 153, 93, 106, 94, 107, 92, 116, 117, 109	,  ⊢
	: , : , : , : , : , :
82	instantiation	105, 106, 139, 93, 107, 98, 94, 125, 103, 116, 117, 109	,  ⊢
	: , : , : , : , : , :
83	instantiation	95, 130, 96	,  ⊢
	: , :
84	axiom		⊢
	proveit.logic.equality.equals_transitivity
85	instantiation	97, 106, 139, 107, 98, 99, 125, 103, 116, 117, 109	,  ⊢
	: , : , : , : , : , : , :
86	instantiation	100, 153, 101, 106, 102, 107, 116, 125, 103, 117, 109	,  ⊢
	: , : , : , : , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
89	theorem		⊢
	proveit.logic.equality.sub_right_side_into
90	instantiation	115, 104, 109	,  ⊢
	: , :
91	instantiation	105, 106, 139, 153, 107, 108, 116, 117, 109	,  ⊢
	: , : , : , : , : , :
92	instantiation	154, 134, 110	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
94	instantiation	111	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
96	instantiation	112, 113	,  ⊢
	:
97	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
98	instantiation	118	⊢
	: , :
99	instantiation	118	⊢
	: , :
100	theorem		⊢
	proveit.numbers.multiplication.association
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
102	instantiation	114	⊢
	: , : , : , :
103	instantiation	154, 134, 121	⊢
	: , : , :
104	instantiation	115, 116, 117	,  ⊢
	: , :
105	theorem		⊢
	proveit.numbers.multiplication.disassociation
106	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
107	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
108	instantiation	118	⊢
	: , :
109	instantiation	154, 134, 119	⊢
	: , : , :
110	instantiation	120, 130, 121	⊢
	: , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
112	theorem		⊢
	proveit.numbers.negation.nat_closure
113	instantiation	122, 141, 123	,  ⊢
	:
114	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
115	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
116	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
117	instantiation	124, 125, 126	,  ⊢
	: , :
118	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
119	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
120	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
121	instantiation	154, 127, 128	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
123	instantiation	129, 145, 146, 143	,  ⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
125	instantiation	154, 134, 130	⊢
	: , : , :
126	instantiation	131, 132	,  ⊢
	:
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
129	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
130	instantiation	154, 137, 133	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.negation.complex_closure
132	instantiation	154, 134, 135	,  ⊢
	: , : , :
133	instantiation	154, 140, 136	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
135	instantiation	154, 137, 138	,  ⊢
	: , : , :
136	instantiation	154, 152, 139	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
138	instantiation	154, 140, 141	,  ⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
140	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
141	instantiation	154, 142, 143	,  ⊢
	: , : , :
142	instantiation	144, 145, 146	⊢
	: , :
143	assumption		⊢
144	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
145	instantiation	147, 148, 149	⊢
	: , :
146	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
147	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
148	instantiation	150, 151	⊢
	:
149	instantiation	154, 152, 153	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.negation.int_closure
151	instantiation	154, 155, 156	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
153	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
154	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
156	assumption		⊢
*equality replacement requirements