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, 147, 148, 4	⊢
	: , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
4	instantiation	6, 7, 127, 85, 8, 9*, 10*	⊢
	: , : , :
5	instantiation	11, 12, 13	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	156, 139, 14	⊢
	: , : , :
8	instantiation	15, 158	⊢
	:
9	instantiation	19, 16, 17, 18	⊢
	: , : , : , :
10	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
11	theorem		⊢
	proveit.logic.equality.sub_left_side_into
12	instantiation	52, 53, 23, 24	,  ⊢
	: , : , : , :
13	instantiation	25, 26	⊢
	: , : , :
14	instantiation	156, 142, 27	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
16	instantiation	93, 28, 29	⊢
	: , : , :
17	instantiation	30, 64, 75, 123, 31	⊢
	: , : , :
18	instantiation	86	⊢
	:
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	93, 32, 33	⊢
	: , : , :
21	instantiation	86	⊢
	:
22	instantiation	34, 35	⊢
	: , :
23	instantiation	36, 59, 37, 38	⊢
	: , :
24	instantiation	39, 53, 40, 41	,  ⊢
	: , : , : , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	42, 123	⊢
	:
27	instantiation	149, 150, 138	⊢
	: , :
28	instantiation	71, 141, 155, 110, 47, 111, 59, 73	⊢
	: , : , : , : , : , :
29	instantiation	93, 43, 44	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
31	instantiation	99, 45, 46	⊢
	: , : , :
32	instantiation	71, 141, 155, 110, 47, 111, 75, 73, 59	⊢
	: , : , : , : , : , :
33	instantiation	74, 75, 59, 76	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.equals_reversal
35	instantiation	48, 59	⊢
	:
36	theorem		⊢
	proveit.numbers.division.div_complex_closure
37	instantiation	49, 123	⊢
	:
38	instantiation	50, 67, 51	⊢
	: , :
39	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
40	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
41	instantiation	52, 53, 54, 55	,  ⊢
	: , : , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43	instantiation	56, 141, 110, 111, 59, 73	⊢
	: , : , : , : , : , : , :
44	instantiation	57, 110, 155, 141, 111, 58, 59, 73, 60*	⊢
	: , : , : , : , : , :
45	instantiation	93, 61, 62	⊢
	: , : , :
46	instantiation	63, 75, 64	⊢
	: , :
47	instantiation	119	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.elim_zero_left
49	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
50	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
51	instantiation	65, 66, 67	⊢
	: , :
52	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
53	instantiation	68, 90	⊢
	:
54	instantiation	122, 69, 70	,  ⊢
	: , :
55	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
56	theorem		⊢
	proveit.numbers.addition.leftward_commutation
57	theorem		⊢
	proveit.numbers.addition.association
58	instantiation	119	⊢
	: , :
59	instantiation	156, 136, 127	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
61	instantiation	71, 141, 155, 110, 72, 111, 75, 73, 123	⊢
	: , : , : , : , : , :
62	instantiation	74, 75, 123, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.commutation
64	instantiation	156, 136, 77	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
66	instantiation	156, 79, 78	⊢
	: , : , :
67	instantiation	156, 79, 80	⊢
	: , : , :
68	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
69	instantiation	156, 136, 81	⊢
	: , : , :
70	instantiation	99, 82, 83	,  ⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.disassociation
72	instantiation	119	⊢
	: , :
73	instantiation	156, 136, 84	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
75	instantiation	156, 136, 85	⊢
	: , : , :
76	instantiation	86	⊢
	:
77	instantiation	156, 139, 87	⊢
	: , : , :
78	instantiation	156, 89, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80	instantiation	156, 89, 90	⊢
	: , : , :
81	instantiation	156, 129, 91	⊢
	: , : , :
82	instantiation	116, 102, 92	,  ⊢
	: , :
83	instantiation	93, 94, 95	,  ⊢
	: , : , :
84	instantiation	156, 139, 96	⊢
	: , : , :
85	instantiation	97, 98, 158	⊢
	: , : , :
86	axiom		⊢
	proveit.logic.equality.equals_reflexivity
87	instantiation	156, 142, 147	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
92	instantiation	99, 100, 101	,  ⊢
	: , : , :
93	axiom		⊢
	proveit.logic.equality.equals_transitivity
94	instantiation	109, 141, 103, 110, 105, 111, 102, 117, 118, 113	,  ⊢
	: , : , : , : , : , :
95	instantiation	109, 110, 155, 103, 111, 104, 105, 123, 114, 117, 118, 113	,  ⊢
	: , : , : , : , : , :
96	instantiation	156, 142, 150	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
98	instantiation	106, 107	⊢
	: , :
99	theorem		⊢
	proveit.logic.equality.sub_right_side_into
100	instantiation	116, 108, 113	,  ⊢
	: , :
101	instantiation	109, 110, 155, 141, 111, 112, 117, 118, 113	,  ⊢
	: , : , : , : , : , :
102	instantiation	116, 123, 114	⊢
	: , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
104	instantiation	119	⊢
	: , :
105	instantiation	115	⊢
	: , : , :
106	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
108	instantiation	116, 117, 118	,  ⊢
	: , :
109	theorem		⊢
	proveit.numbers.multiplication.disassociation
110	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
111	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
112	instantiation	119	⊢
	: , :
113	instantiation	156, 136, 120	⊢
	: , : , :
114	instantiation	156, 136, 121	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
116	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
118	instantiation	122, 123, 124	,  ⊢
	: , :
119	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
120	instantiation	125, 126, 127, 128	⊢
	: , : , :
121	instantiation	156, 129, 130	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
123	instantiation	156, 136, 131	⊢
	: , : , :
124	instantiation	132, 133	,  ⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
127	instantiation	156, 139, 134	⊢
	: , : , :
128	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
131	instantiation	156, 139, 135	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.negation.complex_closure
133	instantiation	156, 136, 137	,  ⊢
	: , : , :
134	instantiation	156, 142, 138	⊢
	: , : , :
135	instantiation	156, 142, 151	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
137	instantiation	156, 139, 140	,  ⊢
	: , : , :
138	instantiation	156, 154, 141	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
140	instantiation	156, 142, 143	,  ⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
142	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
143	instantiation	156, 144, 145	,  ⊢
	: , : , :
144	instantiation	146, 147, 148	⊢
	: , :
145	assumption		⊢
146	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
147	instantiation	149, 150, 151	⊢
	: , :
148	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
149	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
150	instantiation	152, 153	⊢
	:
151	instantiation	156, 154, 155	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.negation.int_closure
153	instantiation	156, 157, 158	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
156	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
157	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
158	assumption		⊢
*equality replacement requirements