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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
2	reference	101	⊢
3	reference	9	⊢
4	instantiation	7, 10, 101	⊢
	: , :
5	instantiation	8, 9, 10, 101, 11, 12	⊢
	: , : , :
6	instantiation	53, 13, 14, 15	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
9	instantiation	121, 112, 16	⊢
	: , : , :
10	instantiation	121, 112, 17	⊢
	: , : , :
11	instantiation	18, 115, 34, 27	⊢
	: , : , :
12	instantiation	19, 120	⊢
	:
13	instantiation	36, 20, 21	⊢
	: , : , :
14	instantiation	39	⊢
	:
15	instantiation	65, 42	⊢
	: , :
16	instantiation	121, 118, 22	⊢
	: , : , :
17	instantiation	121, 118, 34	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
20	instantiation	67, 23	⊢
	: , : , :
21	instantiation	36, 24, 25	⊢
	: , : , :
22	instantiation	121, 26, 27	⊢
	: , : , :
23	instantiation	36, 28, 29	⊢
	: , : , :
24	instantiation	43, 46, 123, 120, 48, 30, 49, 77, 90	⊢
	: , : , : , : , : , :
25	instantiation	31, 90, 49, 32	⊢
	: , : , :
26	instantiation	33, 115, 34	⊢
	: , :
27	assumption		⊢
28	instantiation	67, 35	⊢
	: , : , :
29	instantiation	36, 37, 38	⊢
	: , : , :
30	instantiation	57	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
32	instantiation	39	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
34	instantiation	40, 41, 106	⊢
	: , :
35	instantiation	67, 42	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	43, 46, 123, 120, 48, 44, 49, 74, 90	⊢
	: , : , : , : , : , :
38	instantiation	45, 120, 123, 46, 47, 48, 49, 74, 90, 50*	⊢
	: , : , : , : , : , :
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
41	instantiation	121, 51, 52	⊢
	: , : , :
42	instantiation	53, 54, 55, 56	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.addition.disassociation
44	instantiation	57	⊢
	: , :
45	theorem		⊢
	proveit.numbers.addition.association
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	instantiation	57	⊢
	: , :
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	58, 59, 60	⊢
	: , :
50	instantiation	61, 62, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
53	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
54	instantiation	67, 64	⊢
	: , : , :
55	instantiation	65, 66	⊢
	: , :
56	instantiation	67, 68	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
59	instantiation	69, 90, 70, 71	⊢
	: , :
60	instantiation	83, 96, 76	⊢
	: , :
61	theorem		⊢
	proveit.logic.equality.sub_right_side_into
62	instantiation	72, 90, 96, 73	⊢
	: , : , :
63	instantiation	75, 90, 74	⊢
	: , :
64	instantiation	75, 76, 77	⊢
	: , :
65	theorem		⊢
	proveit.logic.equality.equals_reversal
66	instantiation	78, 96, 79, 88, 85	⊢
	: , : , :
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	80, 81, 82	⊢
	: , :
69	theorem		⊢
	proveit.numbers.division.div_complex_closure
70	instantiation	83, 96, 90	⊢
	: , :
71	instantiation	84, 85, 86	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
73	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
74	instantiation	121, 104, 87	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.commutation
76	instantiation	121, 104, 88	⊢
	: , : , :
77	instantiation	89, 90	⊢
	:
78	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
79	instantiation	91, 101	⊢
	:
80	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
81	instantiation	121, 92, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
83	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
84	theorem		⊢
	proveit.logic.equality.sub_left_side_into
85	instantiation	94, 117	⊢
	:
86	instantiation	95, 96	⊢
	:
87	instantiation	121, 112, 97	⊢
	: , : , :
88	instantiation	98, 99, 100	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.negation.complex_closure
90	instantiation	121, 104, 101	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.negation.real_closure
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
93	instantiation	121, 102, 103	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
95	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
96	instantiation	121, 104, 105	⊢
	: , : , :
97	instantiation	121, 118, 106	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
99	instantiation	107, 108	⊢
	: , :
100	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
101	instantiation	121, 112, 109	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
103	instantiation	121, 110, 111	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
105	instantiation	121, 112, 113	⊢
	: , : , :
106	instantiation	114, 119	⊢
	:
107	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
109	instantiation	121, 118, 115	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
111	instantiation	121, 116, 117	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
113	instantiation	121, 118, 119	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.negation.int_closure
115	instantiation	121, 122, 120	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
119	instantiation	121, 122, 123	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
121	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements