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