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