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