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_right_term_bound
2	reference	33	⊢
3	instantiation	20, 25, 26	⊢
	: , :
4	instantiation	28, 8	⊢
	:
5	instantiation	7, 8, 9, 10, 11*	⊢
	: , :
6	instantiation	12, 89, 100, 13, 14, 15, 16, 17, 18	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
8	instantiation	19, 88	⊢
	:
9	instantiation	20, 27, 29	⊢
	: , :
10	instantiation	21, 88	⊢
	:
11	instantiation	22, 23, 24	⊢
	: , :
12	theorem		⊢
	proveit.numbers.addition.disassociation
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	instantiation	50	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	107, 61, 33	⊢
	: , : , :
17	instantiation	107, 61, 25	⊢
	: , : , :
18	instantiation	107, 61, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.physics.quantum.QPE._pfail_in_real
20	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
21	theorem		⊢
	proveit.physics.quantum.QPE._failure_upper_bound
22	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
23	instantiation	107, 61, 27	⊢
	: , : , :
24	instantiation	107, 61, 29	⊢
	: , : , :
25	instantiation	28, 27	⊢
	:
26	instantiation	28, 29	⊢
	:
27	instantiation	32, 33, 30, 31	⊢
	: , :
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	32, 33, 34, 35	⊢
	: , :
30	instantiation	39, 62, 49	⊢
	: , :
31	instantiation	42, 100, 36, 37, 53	⊢
	: , :
32	theorem		⊢
	proveit.numbers.division.div_real_closure
33	instantiation	107, 68, 38	⊢
	: , : , :
34	instantiation	39, 40, 41	⊢
	: , :
35	instantiation	42, 100, 43, 44, 45	⊢
	: , :
36	instantiation	50	⊢
	: , :
37	instantiation	107, 59, 46	⊢
	: , : , :
38	instantiation	107, 74, 86	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
40	instantiation	107, 68, 47	⊢
	: , : , :
41	instantiation	48, 49, 100	⊢
	: , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
43	instantiation	50	⊢
	: , :
44	instantiation	107, 59, 51	⊢
	: , : , :
45	instantiation	52, 53, 54	⊢
	: , :
46	instantiation	107, 66, 55	⊢
	: , : , :
47	instantiation	107, 74, 56	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
49	instantiation	107, 68, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
51	instantiation	107, 66, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
53	instantiation	107, 59, 60	⊢
	: , : , :
54	instantiation	107, 61, 62	⊢
	: , : , :
55	instantiation	107, 72, 63	⊢
	: , : , :
56	instantiation	107, 99, 64	⊢
	: , : , :
57	instantiation	107, 74, 78	⊢
	: , : , :
58	instantiation	107, 72, 65	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
60	instantiation	107, 66, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	instantiation	107, 68, 69	⊢
	: , : , :
63	instantiation	107, 75, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
65	instantiation	107, 75, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
67	instantiation	107, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	107, 74, 95	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
73	instantiation	107, 75, 76	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
76	instantiation	77, 78, 79	⊢
	:
77	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
78	instantiation	107, 80, 88	⊢
	: , : , :
79	instantiation	81, 82, 83	⊢
	: , : , :
80	instantiation	84, 86, 87	⊢
	: , :
81	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
82	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
83	instantiation	85, 86, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
85	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
86	instantiation	107, 99, 89	⊢
	: , : , :
87	instantiation	101, 90, 91	⊢
	: , :
88	theorem		⊢
	proveit.physics.quantum.QPE._e_value_in_e_domain
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
90	instantiation	92, 95, 93	⊢
	: , :
91	instantiation	94, 95	⊢
	:
92	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
93	instantiation	96, 97, 98	⊢
	:
94	theorem		⊢
	proveit.numbers.negation.int_closure
95	instantiation	107, 99, 100	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
97	instantiation	101, 102, 103	⊢
	: , :
98	instantiation	104, 105	⊢
	: , :
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
101	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
102	instantiation	107, 106, 111	⊢
	: , : , :
103	instantiation	107, 108, 109	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
105	instantiation	110, 111	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
109	instantiation	112, 113	⊢
	:
110	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
111	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
112	theorem		⊢
	proveit.numbers.negation.int_neg_closure
113	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements