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	98	⊢
2	instantiation	103, 4	⊢
	: , : , :
3	instantiation	98, 5, 6	⊢
	: , : , :
4	instantiation	98, 7, 8	⊢
	: , : , :
5	instantiation	123, 189, 184, 124, 9, 125, 46, 11	⊢
	: , : , : , : , : , :
6	instantiation	44, 124, 184, 189, 125, 10, 46, 11, 12*	⊢
	: , : , : , : , : , :
7	instantiation	103, 13	⊢
	: , : , :
8	instantiation	98, 14, 15	⊢
	: , : , :
9	instantiation	140	⊢
	: , :
10	instantiation	140	⊢
	: , :
11	modus ponens	16, 36	⊢
12	instantiation	17, 46, 165, 18*, 19*	⊢
	: , : , :
13	modus ponens	20, 21	⊢
14	instantiation	103, 22	⊢
	: , : , :
15	instantiation	23, 24	⊢
	: , :
16	instantiation	25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
18	instantiation	132, 46	⊢
	:
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
20	instantiation	26, 165	⊢
	: , : , : , : , : , :
21	generalization	27	⊢
22	modus ponens	28, 29	⊢
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	30, 125, 46	⊢
	: , :
25	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
26	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
27	instantiation	31, 32	⊢
	: , : , :
28	instantiation	33, 165	⊢
	: , : , : , : , : , : , :
29	generalization	34	⊢
30	modus ponens	35, 36	⊢
31	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
32	deduction	37	⊢
33	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
34	instantiation	98, 38, 39	,  ⊢
	: , : , :
35	instantiation	40, 189, 165, 124	⊢
	: , : , : , : , : , :
36	generalization	41	⊢
37	instantiation	123, 189, 184, 124, 42, 125, 47, 46, 48	,  ⊢
	: , : , : , : , : , :
38	instantiation	43, 124, 189, 125, 47, 46, 48	,  ⊢
	: , : , : , : , : , : , :
39	instantiation	44, 189, 184, 124, 45, 125, 46, 47, 48	,  ⊢
	: , : , : , : , : , :
40	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
41	instantiation	137, 47, 48	,  ⊢
	: , :
42	instantiation	140	⊢
	: , :
43	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
44	theorem		⊢
	proveit.numbers.multiplication.association
45	instantiation	140	⊢
	: , :
46	instantiation	74, 49, 50, 51	⊢
	: , :
47	instantiation	56, 53, 52	⊢
	: , :
48	instantiation	56, 53, 54	,  ⊢
	: , :
49	instantiation	187, 150, 55	⊢
	: , : , :
50	instantiation	56, 133, 57	⊢
	: , :
51	instantiation	58, 59, 60	⊢
	: , : , :
52	instantiation	109, 61, 62	⊢
	: , : , :
53	instantiation	187, 150, 63	⊢
	: , : , :
54	instantiation	64, 65	,  ⊢
	:
55	instantiation	187, 161, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
57	instantiation	74, 106, 133, 81	⊢
	: , :
58	theorem		⊢
	proveit.logic.equality.sub_left_side_into
59	instantiation	67, 144, 68	⊢
	: , :
60	instantiation	103, 69	⊢
	: , : , :
61	instantiation	137, 112, 70	⊢
	: , :
62	instantiation	98, 71, 72	⊢
	: , : , :
63	instantiation	187, 153, 73	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.complex_closure
65	instantiation	74, 75, 76, 77	,  ⊢
	: , :
66	instantiation	187, 168, 183	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
68	instantiation	187, 78, 79	⊢
	: , : , :
69	instantiation	80, 106, 133, 81, 82*	⊢
	: , :
70	instantiation	109, 83, 84	⊢
	: , : , :
71	instantiation	123, 189, 113, 124, 85, 125, 112, 138, 108, 139	⊢
	: , : , : , : , : , :
72	instantiation	123, 124, 184, 113, 125, 114, 85, 133, 128, 138, 108, 139	⊢
	: , : , : , : , : , :
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
74	theorem		⊢
	proveit.numbers.division.div_complex_closure
75	instantiation	109, 86, 87	,  ⊢
	: , : , :
76	instantiation	187, 150, 88	⊢
	: , : , :
77	instantiation	92, 89	⊢
	:
78	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
79	instantiation	90, 149, 91	⊢
	: , :
80	theorem		⊢
	proveit.numbers.division.div_as_mult
81	instantiation	92, 167	⊢
	:
82	instantiation	98, 93, 94	⊢
	: , : , :
83	instantiation	137, 95, 139	⊢
	: , :
84	instantiation	123, 124, 184, 189, 125, 96, 138, 108, 139	⊢
	: , : , : , : , : , :
85	instantiation	129	⊢
	: , : , :
86	instantiation	137, 112, 97	,  ⊢
	: , :
87	instantiation	98, 99, 100	,  ⊢
	: , : , :
88	instantiation	187, 161, 101	⊢
	: , : , :
89	instantiation	102, 184, 181	⊢
	: , :
90	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
91	instantiation	187, 166, 186	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
93	instantiation	103, 104	⊢
	: , : , :
94	instantiation	105, 106, 107	⊢
	: , :
95	instantiation	137, 138, 108	⊢
	: , :
96	instantiation	140	⊢
	: , :
97	instantiation	109, 110, 111	,  ⊢
	: , : , :
98	axiom		⊢
	proveit.logic.equality.equals_transitivity
99	instantiation	123, 189, 113, 124, 115, 125, 112, 138, 139, 127	,  ⊢
	: , : , : , : , : , :
100	instantiation	123, 124, 184, 113, 125, 114, 115, 133, 128, 138, 139, 127	,  ⊢
	: , : , : , : , : , :
101	instantiation	187, 168, 177	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
103	axiom		⊢
	proveit.logic.equality.substitution
104	instantiation	116, 117, 165, 118*	⊢
	: , :
105	theorem		⊢
	proveit.numbers.multiplication.commutation
106	instantiation	187, 150, 119	⊢
	: , : , :
107	instantiation	187, 150, 120	⊢
	: , : , :
108	instantiation	187, 150, 121	⊢
	: , : , :
109	theorem		⊢
	proveit.logic.equality.sub_right_side_into
110	instantiation	137, 122, 127	,  ⊢
	: , :
111	instantiation	123, 124, 184, 189, 125, 126, 138, 139, 127	,  ⊢
	: , : , : , : , : , :
112	instantiation	137, 133, 128	⊢
	: , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
114	instantiation	140	⊢
	: , :
115	instantiation	129	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
117	instantiation	187, 130, 131	⊢
	: , : , :
118	instantiation	132, 133	⊢
	:
119	instantiation	134, 135, 186	⊢
	: , : , :
120	instantiation	187, 161, 136	⊢
	: , : , :
121	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
122	instantiation	137, 138, 139	⊢
	: , :
123	theorem		⊢
	proveit.numbers.multiplication.disassociation
124	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
125	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
126	instantiation	140	⊢
	: , :
127	instantiation	187, 150, 141	⊢
	: , : , :
128	instantiation	187, 150, 142	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
130	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
131	instantiation	187, 143, 144	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
133	instantiation	187, 150, 145	⊢
	: , : , :
134	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
135	instantiation	146, 147	⊢
	: , :
136	instantiation	187, 148, 149	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
138	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
139	instantiation	187, 150, 151	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
141	instantiation	187, 161, 152	⊢
	: , : , :
142	instantiation	187, 153, 154	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
144	instantiation	187, 155, 156	⊢
	: , : , :
145	instantiation	187, 161, 157	⊢
	: , : , :
146	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
148	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
149	instantiation	158, 159, 160	⊢
	: , :
150	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
151	instantiation	187, 161, 162	⊢
	: , : , :
152	instantiation	187, 168, 163	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
155	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
156	instantiation	187, 164, 167	⊢
	: , : , :
157	instantiation	187, 168, 180	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
159	instantiation	187, 166, 165	⊢
	: , : , :
160	instantiation	187, 166, 167	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
162	instantiation	187, 168, 169	⊢
	: , : , :
163	instantiation	187, 171, 170	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
165	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
166	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
167	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
169	instantiation	187, 171, 172	⊢
	: , : , :
170	assumption		⊢
171	instantiation	173, 174, 175	⊢
	: , :
172	assumption		⊢
173	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
174	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
175	instantiation	176, 177, 178	⊢
	: , :
176	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
177	instantiation	179, 180, 181	⊢
	: , :
178	instantiation	182, 183	⊢
	:
179	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
180	instantiation	187, 188, 184	⊢
	: , : , :
181	instantiation	187, 185, 186	⊢
	: , : , :
182	theorem		⊢
	proveit.numbers.negation.int_closure
183	instantiation	187, 188, 189	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
185	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
186	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
187	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
188	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
189	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements