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	⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.rhs_via_equality
2	deduction	4	⊢
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 8, 9	,  ⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	10	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
8	instantiation	11, 15	⊢
	: , :
9	instantiation	12, 13, 14, 15	,  ⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.not_equals_def
11	theorem		⊢
	proveit.logic.equality.unfold_not_equals
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval
13	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
14	instantiation	39, 16, 17, 18, 19	⊢
	: , : , :
15	assumption		⊢
16	instantiation	63, 103, 96	⊢
	: , :
17	instantiation	63, 103, 104	⊢
	: , :
18	instantiation	20, 96, 104, 30	⊢
	: , : , :
19	instantiation	43, 21, 22	⊢
	: , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
21	instantiation	25, 23, 24	⊢
	: , : , :
22	instantiation	25, 26, 27	⊢
	: , : , :
23	instantiation	28, 96, 104, 30	⊢
	: , : , :
24	instantiation	31, 77	⊢
	:
25	theorem		⊢
	proveit.logic.equality.sub_left_side_into
26	instantiation	29, 96, 104, 30	⊢
	: , : , :
27	instantiation	31, 78	⊢
	:
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
30	instantiation	32, 33	⊢
	:
31	theorem		⊢
	proveit.numbers.addition.elim_zero_left
32	instantiation	34, 156, 35, 36, 37	⊢
	: , : , : , :
33	assumption		⊢
34	theorem		⊢
	proveit.logic.sets.enumeration.true_for_each_then_true_for_all
35	instantiation	134	⊢
	: , :
36	instantiation	39, 96, 104, 97, 38	⊢
	: , : , :
37	instantiation	39, 96, 104, 100, 40	⊢
	: , : , :
38	instantiation	43, 41, 42	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
40	instantiation	43, 44, 45	⊢
	: , :
41	instantiation	50, 96, 103, 46, 47, 48*, 49*	⊢
	: , : , :
42	instantiation	93, 103, 104, 105	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
44	instantiation	50, 114, 51, 52, 53*, 54*	⊢
	: , : , :
45	instantiation	58, 55, 67	⊢
	: , : , :
46	instantiation	63, 97, 104	⊢
	: , :
47	instantiation	64, 103, 97, 104, 56, 57	⊢
	: , : , :
48	instantiation	58, 59, 60	⊢
	: , : , :
49	instantiation	117, 61, 62	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
51	instantiation	63, 100, 124	⊢
	: , :
52	instantiation	64, 114, 100, 124, 65, 95	⊢
	: , : , :
53	instantiation	66, 90, 78, 67	⊢
	: , : , :
54	instantiation	117, 68, 69	⊢
	: , : , :
55	instantiation	70, 100, 124, 71, 72	⊢
	: , : , :
56	instantiation	81, 103, 104, 105	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	73, 77	⊢
	:
60	instantiation	74, 77, 75	⊢
	: , :
61	instantiation	84, 85, 156, 133, 86, 76, 79, 78, 77	⊢
	: , : , : , : , : , :
62	instantiation	89, 78, 79, 80	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
64	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
65	instantiation	81, 114, 124, 115	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
67	instantiation	82, 125, 153, 83*	⊢
	: , : , : , :
68	instantiation	84, 85, 156, 133, 86, 87, 91, 90, 88	⊢
	: , : , : , : , : , :
69	instantiation	89, 90, 91, 92	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.ordering.less_add_right
71	instantiation	93, 114, 124, 115	⊢
	: , : , :
72	instantiation	94, 95	⊢
	: , :
73	theorem		⊢
	proveit.numbers.addition.elim_zero_right
74	theorem		⊢
	proveit.numbers.addition.commutation
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
76	instantiation	134	⊢
	: , :
77	instantiation	154, 141, 96	⊢
	: , : , :
78	instantiation	154, 141, 104	⊢
	: , : , :
79	instantiation	154, 141, 97	⊢
	: , : , :
80	instantiation	101	⊢
	:
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
82	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
83	instantiation	117, 98, 99	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.addition.disassociation
85	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
86	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
87	instantiation	134	⊢
	: , :
88	instantiation	154, 141, 114	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
90	instantiation	154, 141, 124	⊢
	: , : , :
91	instantiation	154, 141, 100	⊢
	: , : , :
92	instantiation	101	⊢
	:
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
94	theorem		⊢
	proveit.numbers.ordering.relax_less
95	instantiation	102, 140	⊢
	:
96	instantiation	123, 104	⊢
	:
97	instantiation	113, 103, 104, 105	⊢
	: , : , :
98	instantiation	126, 156, 106, 107, 108, 109	⊢
	: , : , : , :
99	instantiation	110, 111, 112	⊢
	:
100	instantiation	113, 114, 124, 115	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
104	instantiation	154, 147, 116	⊢
	: , : , :
105	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
106	instantiation	134	⊢
	: , :
107	instantiation	134	⊢
	: , :
108	instantiation	117, 118, 119	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
110	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
111	instantiation	154, 141, 120	⊢
	: , : , :
112	instantiation	121, 122	⊢
	:
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
114	instantiation	123, 124	⊢
	:
115	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
116	instantiation	154, 152, 125	⊢
	: , : , :
117	axiom		⊢
	proveit.logic.equality.equals_transitivity
118	instantiation	126, 156, 127, 128, 129, 130	⊢
	: , : , : , :
119	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
120	instantiation	154, 147, 131	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
122	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
123	theorem		⊢
	proveit.numbers.negation.real_closure
124	instantiation	154, 147, 132	⊢
	: , : , :
125	instantiation	154, 155, 133	⊢
	: , : , :
126	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
127	instantiation	134	⊢
	: , :
128	instantiation	134	⊢
	: , :
129	instantiation	135, 137	⊢
	:
130	instantiation	136, 137	⊢
	:
131	instantiation	154, 152, 138	⊢
	: , : , :
132	instantiation	154, 139, 140	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
134	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
135	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
137	instantiation	154, 141, 142	⊢
	: , : , :
138	instantiation	154, 155, 143	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
140	instantiation	144, 145, 146	⊢
	: , :
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
142	instantiation	154, 147, 148	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
144	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
145	instantiation	154, 150, 149	⊢
	: , : , :
146	instantiation	154, 150, 151	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
148	instantiation	154, 152, 153	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
150	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
151	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
152	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
153	instantiation	154, 155, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements