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