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	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	81, 5, 6	⊢
	: , : , :
3	instantiation	28	⊢
	:
4	instantiation	37, 7	⊢
	: , :
5	instantiation	81, 8, 9	⊢
	: , : , :
6	instantiation	81, 10, 11	⊢
	: , : , :
7	instantiation	98, 12	⊢
	: , : , :
8	instantiation	98, 13	⊢
	: , : , :
9	instantiation	98, 14	⊢
	: , : , :
10	instantiation	15, 155, 152, 73, 16, 74, 76, 17, 19	⊢
	: , : , : , : , : , :
11	instantiation	18, 76, 19, 20	⊢
	: , : , :
12	instantiation	81, 21, 22	⊢
	: , : , :
13	instantiation	81, 23, 24	⊢
	: , : , :
14	instantiation	98, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.disassociation
16	instantiation	106	⊢
	: , :
17	instantiation	153, 143, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
19	instantiation	129, 27	⊢
	:
20	instantiation	28	⊢
	:
21	instantiation	98, 29	⊢
	: , : , :
22	instantiation	64, 126, 30, 31, 32*	⊢
	: , :
23	instantiation	98, 33	⊢
	: , : , :
24	instantiation	34, 148, 140, 35*	⊢
	: , : , : , :
25	instantiation	98, 36	⊢
	: , : , :
26	instantiation	123, 90	⊢
	:
27	instantiation	39, 76, 100	⊢
	: , :
28	axiom		⊢
	proveit.logic.equality.equals_reflexivity
29	instantiation	37, 38	⊢
	: , :
30	instantiation	39, 116, 68	⊢
	: , :
31	instantiation	40, 152, 41, 87, 42	⊢
	: , :
32	instantiation	81, 43, 44	⊢
	: , : , :
33	instantiation	45, 126, 87, 46*, 47*	⊢
	: , : , : , :
34	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
35	instantiation	81, 48, 49	⊢
	: , : , :
36	instantiation	98, 50	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.equality.equals_reversal
38	instantiation	51, 116, 88, 151, 89*	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
40	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
41	instantiation	106	⊢
	: , :
42	instantiation	153, 102, 52	⊢
	: , : , :
43	instantiation	98, 53	⊢
	: , : , :
44	instantiation	81, 54, 55	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.division.prod_of_fracs
46	instantiation	135, 126	⊢
	:
47	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
48	instantiation	91, 152, 56, 57, 58, 59	⊢
	: , : , : , :
49	instantiation	60, 61, 87, 126, 62*, 63*	⊢
	: , : , :
50	instantiation	64, 126, 68, 69, 65*	⊢
	: , :
51	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
52	instantiation	153, 118, 66	⊢
	: , : , :
53	instantiation	67, 116, 68, 112, 113, 69, 70*, 99*	⊢
	: , : , :
54	instantiation	71, 155, 152, 73, 75, 74, 126, 76, 100	⊢
	: , : , : , : , : , :
55	instantiation	72, 73, 152, 74, 75, 76, 100	⊢
	: , : , : , :
56	instantiation	106	⊢
	: , :
57	instantiation	106	⊢
	: , :
58	instantiation	81, 77, 78	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
60	theorem		⊢
	proveit.numbers.division.frac_cancel_left
61	instantiation	153, 102, 79	⊢
	: , : , :
62	instantiation	135, 80	⊢
	:
63	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
64	theorem		⊢
	proveit.numbers.division.div_as_mult
65	instantiation	81, 82, 83	⊢
	: , : , :
66	instantiation	153, 130, 84	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
68	instantiation	153, 143, 85	⊢
	: , : , :
69	instantiation	124, 101	⊢
	:
70	instantiation	86, 87, 88, 89*	⊢
	: , :
71	theorem		⊢
	proveit.numbers.multiplication.disassociation
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
73	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
74	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
75	instantiation	106	⊢
	: , :
76	instantiation	153, 143, 90	⊢
	: , : , :
77	instantiation	91, 152, 92, 93, 94, 95	⊢
	: , : , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
79	instantiation	153, 118, 96	⊢
	: , : , :
80	instantiation	153, 143, 97	⊢
	: , : , :
81	axiom		⊢
	proveit.logic.equality.equals_transitivity
82	instantiation	98, 99	⊢
	: , : , :
83	instantiation	107, 100	⊢
	:
84	instantiation	153, 138, 101	⊢
	: , : , :
85	instantiation	149, 150, 101	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
87	instantiation	153, 102, 103	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
89	instantiation	104, 116	⊢
	:
90	instantiation	105, 134, 128, 113	⊢
	: , :
91	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
92	instantiation	106	⊢
	: , :
93	instantiation	106	⊢
	: , :
94	instantiation	107, 108	⊢
	:
95	instantiation	135, 108	⊢
	:
96	instantiation	153, 130, 109	⊢
	: , : , :
97	instantiation	153, 141, 110	⊢
	: , : , :
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	111, 116, 144, 112, 113, 114*	⊢
	: , : , :
100	instantiation	115, 116, 117	⊢
	: , :
101	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
103	instantiation	153, 118, 119	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
105	theorem		⊢
	proveit.numbers.division.div_real_closure
106	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
107	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
108	instantiation	153, 143, 120	⊢
	: , : , :
109	instantiation	153, 138, 121	⊢
	: , : , :
110	instantiation	153, 147, 122	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
112	instantiation	123, 134	⊢
	:
113	instantiation	124, 139	⊢
	:
114	instantiation	125, 136, 126, 127*	⊢
	: , :
115	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
116	instantiation	153, 143, 128	⊢
	: , : , :
117	instantiation	129, 136	⊢
	:
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
119	instantiation	153, 130, 131	⊢
	: , : , :
120	instantiation	153, 141, 132	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
122	instantiation	153, 154, 133	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.negation.real_closure
124	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
125	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
126	instantiation	153, 143, 134	⊢
	: , : , :
127	instantiation	135, 136	⊢
	:
128	instantiation	153, 141, 137	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.negation.complex_closure
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
131	instantiation	153, 138, 139	⊢
	: , : , :
132	instantiation	153, 147, 140	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
134	instantiation	153, 141, 142	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
136	instantiation	153, 143, 144	⊢
	: , : , :
137	instantiation	153, 147, 145	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
140	instantiation	153, 154, 146	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
142	instantiation	153, 147, 148	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
144	instantiation	149, 150, 151	⊢
	: , : , :
145	instantiation	153, 154, 152	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
148	instantiation	153, 154, 155	⊢
	: , : , :
149	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
150	instantiation	156, 157	⊢
	: , :
151	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
153	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
156	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements