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