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