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