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	68	⊢
3	instantiation	7, 8, 58, 9	⊢
	: , :
4	instantiation	16, 37, 35	⊢
	: , :
5	instantiation	10, 11, 12	⊢
	: , : , :
6	instantiation	13, 14, 15	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
8	instantiation	16, 17, 18	⊢
	: , :
9	instantiation	19, 54, 20	⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.sub_right_side_into
11	assumption		⊢
12	axiom		⊢
	proveit.physics.quantum.QPE._best_floor_def
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	21, 22, 84, 89, 23, 24, 28, 25, 27	⊢
	: , : , : , : , : , :
15	instantiation	26, 27, 28, 29	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
17	instantiation	87, 75, 30	⊢
	: , : , :
18	instantiation	31, 32	⊢
	:
19	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
20	instantiation	87, 60, 33	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	34	⊢
	: , :
25	instantiation	87, 36, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
27	instantiation	87, 36, 68	⊢
	: , : , :
28	instantiation	87, 36, 37	⊢
	: , : , :
29	instantiation	38	⊢
	:
30	instantiation	87, 82, 39	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.negation.real_closure
32	instantiation	87, 75, 40	⊢
	: , : , :
33	instantiation	87, 70, 86	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	instantiation	87, 75, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	87, 75, 42	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.equals_reflexivity
39	instantiation	87, 43, 44	⊢
	: , : , :
40	instantiation	87, 82, 45	⊢
	: , : , :
41	instantiation	87, 82, 56	⊢
	: , : , :
42	instantiation	87, 46, 47	⊢
	: , : , :
43	instantiation	48, 49, 50	⊢
	: , :
44	assumption		⊢
45	instantiation	51, 52	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
47	instantiation	53, 54, 55	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
49	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
50	instantiation	62, 74, 56	⊢
	: , :
51	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
52	instantiation	57, 58, 59	⊢
	: , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
54	instantiation	87, 60, 61	⊢
	: , : , :
55	instantiation	62, 63, 64	⊢
	: , :
56	instantiation	72, 83	⊢
	:
57	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
58	instantiation	87, 75, 65	⊢
	: , : , :
59	instantiation	66, 67, 68, 69	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	87, 70, 71	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
63	instantiation	87, 77, 86	⊢
	: , : , :
64	instantiation	72, 73	⊢
	:
65	instantiation	87, 82, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
68	instantiation	87, 75, 76	⊢
	: , : , :
69	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
72	theorem		⊢
	proveit.numbers.negation.int_closure
73	instantiation	87, 77, 78	⊢
	: , : , :
74	instantiation	79, 80, 81	⊢
	: , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	87, 82, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
78	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
79	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
80	instantiation	87, 88, 84	⊢
	: , : , :
81	instantiation	87, 85, 86	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	87, 88, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
86	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
87	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements