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.number_sets.integers.in_interval
2	reference	98	⊢
3	instantiation	109, 6	⊢
	:
4	reference	91	⊢
5	instantiation	7, 8, 9	, ,  ⊢
	: , :
6	instantiation	105, 92, 104	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	10, 98, 107, 95	⊢
	: , : , :
9	instantiation	11, 72, 86, 12, 13, 14*, 15*	, ,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
11	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
12	instantiation	16, 17, 19	, ,  ⊢
	: , : , :
13	instantiation	18, 19	, ,  ⊢
	:
14	instantiation	40, 20, 21	⊢
	: , : , :
15	instantiation	35, 22	,  ⊢
	: , :
16	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
17	instantiation	23, 24	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
19	instantiation	25, 26	, ,  ⊢
	:
20	instantiation	60, 108, 115, 65, 62, 66, 77, 68, 69	⊢
	: , : , : , : , : , :
21	instantiation	27, 77, 68, 28	⊢
	: , : , :
22	instantiation	50, 29, 30, 31	,  ⊢
	: , : , : , :
23	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
25	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
26	instantiation	32, 33, 34	, ,  ⊢
	:
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
28	instantiation	57	⊢
	:
29	instantiation	58, 75, 77	⊢
	: , :
30	instantiation	57	⊢
	:
31	instantiation	35, 36	,  ⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
33	instantiation	105, 92, 91	,  ⊢
	: , :
34	instantiation	37, 82, 83, 74, 38, 39*	, ,  ⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.equals_reversal
36	instantiation	40, 41, 42	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
38	instantiation	43, 44, 45	,  ⊢
	: , : , :
39	instantiation	46, 68, 47	⊢
	: , :
40	axiom		⊢
	proveit.logic.equality.equals_transitivity
41	instantiation	48, 49	,  ⊢
	: , : , :
42	instantiation	50, 51, 52, 53	,  ⊢
	: , : , : , :
43	theorem		⊢
	proveit.logic.equality.sub_right_side_into
44	instantiation	54, 100	⊢
	: , :
45	instantiation	55, 95, 56*	,  ⊢
	:
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
47	instantiation	57	⊢
	:
48	axiom		⊢
	proveit.logic.equality.substitution
49	instantiation	58, 75, 68	,  ⊢
	: , :
50	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
51	instantiation	60, 65, 115, 108, 66, 61, 67, 63, 59	,  ⊢
	: , : , : , : , : , :
52	instantiation	60, 115, 65, 61, 62, 66, 67, 63, 68, 69	,  ⊢
	: , : , : , : , : , :
53	instantiation	64, 108, 65, 66, 67, 68, 69	,  ⊢
	: , : , : , : , : , : , : , :
54	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
55	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
56	instantiation	70, 71	⊢
	:
57	axiom		⊢
	proveit.logic.equality.equals_reflexivity
58	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
59	instantiation	113, 84, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.disassociation
61	instantiation	73	⊢
	: , :
62	instantiation	73	⊢
	: , :
63	instantiation	113, 84, 74	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
65	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
66	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
67	instantiation	76, 75	⊢
	:
68	instantiation	113, 84, 82	⊢
	: , : , :
69	instantiation	76, 77	⊢
	:
70	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
71	instantiation	78, 79	⊢
	: , :
72	instantiation	80, 82, 81	⊢
	: , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
74	instantiation	85, 82	⊢
	:
75	instantiation	113, 84, 83	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.negation.complex_closure
77	instantiation	113, 84, 86	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.ordering.relax_less
79	assumption		⊢
80	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
81	instantiation	85, 86	⊢
	:
82	instantiation	113, 89, 87	⊢
	: , : , :
83	instantiation	113, 89, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	theorem		⊢
	proveit.numbers.negation.real_closure
86	instantiation	113, 89, 90	⊢
	: , : , :
87	instantiation	113, 93, 91	⊢
	: , : , :
88	instantiation	113, 93, 92	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
90	instantiation	113, 93, 104	⊢
	: , : , :
91	instantiation	113, 94, 95	⊢
	: , : , :
92	instantiation	113, 96, 97	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
94	instantiation	101, 98, 107	⊢
	: , :
95	instantiation	99, 100	⊢
	: , :
96	instantiation	101, 104, 102	⊢
	: , :
97	assumption		⊢
98	instantiation	105, 103, 104	⊢
	: , :
99	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
100	assumption		⊢
101	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
102	instantiation	105, 107, 106	⊢
	: , :
103	instantiation	109, 107	⊢
	:
104	instantiation	113, 114, 108	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
106	instantiation	109, 110	⊢
	:
107	instantiation	113, 111, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
109	theorem		⊢
	proveit.numbers.negation.int_closure
110	instantiation	113, 114, 115	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
112	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
113	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements