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	84	⊢
2	instantiation	89, 4	⊢
	: , : , :
3	instantiation	84, 5, 6	⊢
	: , : , :
4	modus ponens	7, 8	⊢
5	instantiation	89, 9	⊢
	: , : , :
6	instantiation	10, 11	⊢
	: , :
7	instantiation	12, 151	⊢
	: , : , : , : , : , :
8	generalization	13	⊢
9	modus ponens	14, 15	⊢
10	theorem		⊢
	proveit.logic.equality.equals_reversal
11	instantiation	16, 111, 32	⊢
	: , :
12	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
13	instantiation	17, 18	⊢
	: , : , :
14	instantiation	19, 151	⊢
	: , : , : , : , : , : , :
15	generalization	20	⊢
16	modus ponens	21, 22	⊢
17	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
18	deduction	23	⊢
19	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
20	instantiation	84, 24, 25	,  ⊢
	: , : , :
21	instantiation	26, 175, 151, 110	⊢
	: , : , : , : , : , :
22	generalization	27	⊢
23	instantiation	109, 175, 170, 110, 28, 111, 33, 32, 34	,  ⊢
	: , : , : , : , : , :
24	instantiation	29, 110, 175, 111, 33, 32, 34	,  ⊢
	: , : , : , : , : , : , :
25	instantiation	30, 175, 170, 110, 31, 111, 32, 33, 34	,  ⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
27	instantiation	123, 33, 34	,  ⊢
	: , :
28	instantiation	126	⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
30	theorem		⊢
	proveit.numbers.multiplication.association
31	instantiation	126	⊢
	: , :
32	instantiation	60, 35, 36, 37	⊢
	: , :
33	instantiation	42, 39, 38	⊢
	: , :
34	instantiation	42, 39, 40	,  ⊢
	: , :
35	instantiation	173, 136, 41	⊢
	: , : , :
36	instantiation	42, 119, 43	⊢
	: , :
37	instantiation	44, 45, 46	⊢
	: , : , :
38	instantiation	95, 47, 48	⊢
	: , : , :
39	instantiation	173, 136, 49	⊢
	: , : , :
40	instantiation	50, 51	,  ⊢
	:
41	instantiation	173, 147, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
43	instantiation	60, 92, 119, 67	⊢
	: , :
44	theorem		⊢
	proveit.logic.equality.sub_left_side_into
45	instantiation	53, 130, 54	⊢
	: , :
46	instantiation	89, 55	⊢
	: , : , :
47	instantiation	123, 98, 56	⊢
	: , :
48	instantiation	84, 57, 58	⊢
	: , : , :
49	instantiation	173, 139, 59	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.negation.complex_closure
51	instantiation	60, 61, 62, 63	,  ⊢
	: , :
52	instantiation	173, 154, 169	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
54	instantiation	173, 64, 65	⊢
	: , : , :
55	instantiation	66, 92, 119, 67, 68*	⊢
	: , :
56	instantiation	95, 69, 70	⊢
	: , : , :
57	instantiation	109, 175, 99, 110, 71, 111, 98, 124, 94, 125	⊢
	: , : , : , : , : , :
58	instantiation	109, 110, 170, 99, 111, 100, 71, 119, 114, 124, 94, 125	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
60	theorem		⊢
	proveit.numbers.division.div_complex_closure
61	instantiation	95, 72, 73	,  ⊢
	: , : , :
62	instantiation	173, 136, 74	⊢
	: , : , :
63	instantiation	78, 75	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
65	instantiation	76, 135, 77	⊢
	: , :
66	theorem		⊢
	proveit.numbers.division.div_as_mult
67	instantiation	78, 153	⊢
	:
68	instantiation	84, 79, 80	⊢
	: , : , :
69	instantiation	123, 81, 125	⊢
	: , :
70	instantiation	109, 110, 170, 175, 111, 82, 124, 94, 125	⊢
	: , : , : , : , : , :
71	instantiation	115	⊢
	: , : , :
72	instantiation	123, 98, 83	,  ⊢
	: , :
73	instantiation	84, 85, 86	,  ⊢
	: , : , :
74	instantiation	173, 147, 87	⊢
	: , : , :
75	instantiation	88, 170, 167	⊢
	: , :
76	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
77	instantiation	173, 152, 172	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
79	instantiation	89, 90	⊢
	: , : , :
80	instantiation	91, 92, 93	⊢
	: , :
81	instantiation	123, 124, 94	⊢
	: , :
82	instantiation	126	⊢
	: , :
83	instantiation	95, 96, 97	,  ⊢
	: , : , :
84	axiom		⊢
	proveit.logic.equality.equals_transitivity
85	instantiation	109, 175, 99, 110, 101, 111, 98, 124, 125, 113	,  ⊢
	: , : , : , : , : , :
86	instantiation	109, 110, 170, 99, 111, 100, 101, 119, 114, 124, 125, 113	,  ⊢
	: , : , : , : , : , :
87	instantiation	173, 154, 163	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
89	axiom		⊢
	proveit.logic.equality.substitution
90	instantiation	102, 103, 151, 104*	⊢
	: , :
91	theorem		⊢
	proveit.numbers.multiplication.commutation
92	instantiation	173, 136, 105	⊢
	: , : , :
93	instantiation	173, 136, 106	⊢
	: , : , :
94	instantiation	173, 136, 107	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.equality.sub_right_side_into
96	instantiation	123, 108, 113	,  ⊢
	: , :
97	instantiation	109, 110, 170, 175, 111, 112, 124, 125, 113	,  ⊢
	: , : , : , : , : , :
98	instantiation	123, 119, 114	⊢
	: , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
100	instantiation	126	⊢
	: , :
101	instantiation	115	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
103	instantiation	173, 116, 117	⊢
	: , : , :
104	instantiation	118, 119	⊢
	:
105	instantiation	120, 121, 172	⊢
	: , : , :
106	instantiation	173, 147, 122	⊢
	: , : , :
107	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
108	instantiation	123, 124, 125	⊢
	: , :
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	126	⊢
	: , :
113	instantiation	173, 136, 127	⊢
	: , : , :
114	instantiation	173, 136, 128	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
116	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
117	instantiation	173, 129, 130	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
119	instantiation	173, 136, 131	⊢
	: , : , :
120	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
121	instantiation	132, 133	⊢
	: , :
122	instantiation	173, 134, 135	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
124	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
125	instantiation	173, 136, 137	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
127	instantiation	173, 147, 138	⊢
	: , : , :
128	instantiation	173, 139, 140	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
130	instantiation	173, 141, 142	⊢
	: , : , :
131	instantiation	173, 147, 143	⊢
	: , : , :
132	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
135	instantiation	144, 145, 146	⊢
	: , :
136	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
137	instantiation	173, 147, 148	⊢
	: , : , :
138	instantiation	173, 154, 149	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
142	instantiation	173, 150, 153	⊢
	: , : , :
143	instantiation	173, 154, 166	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
145	instantiation	173, 152, 151	⊢
	: , : , :
146	instantiation	173, 152, 153	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
148	instantiation	173, 154, 155	⊢
	: , : , :
149	instantiation	173, 157, 156	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
151	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
152	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
153	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
155	instantiation	173, 157, 158	⊢
	: , : , :
156	assumption		⊢
157	instantiation	159, 160, 161	⊢
	: , :
158	assumption		⊢
159	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
160	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
161	instantiation	162, 163, 164	⊢
	: , :
162	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
163	instantiation	165, 166, 167	⊢
	: , :
164	instantiation	168, 169	⊢
	:
165	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
166	instantiation	173, 174, 170	⊢
	: , : , :
167	instantiation	173, 171, 172	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.negation.int_closure
169	instantiation	173, 174, 175	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
171	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
172	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
173	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
175	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements