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.strong_bound_via_left_term_bound
2	reference	45	⊢
3	instantiation	7, 38, 56	⊢
	: , :
4	instantiation	8, 45, 38, 56, 9, 10	⊢
	: , : , :
5	instantiation	11, 12, 13, 14	⊢
	: , : , : , :
6	instantiation	59, 15, 16	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.ordering.less_add_right
9	instantiation	17, 45, 56, 46	⊢
	: , : , :
10	instantiation	18, 19	⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
12	instantiation	20, 30, 43, 21	⊢
	: , : , :
13	instantiation	39	⊢
	:
14	instantiation	22, 23	⊢
	: , :
15	instantiation	24, 25, 97, 81, 26, 27, 31, 30, 28	⊢
	: , : , : , : , : , :
16	instantiation	29, 30, 31, 32	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
18	theorem		⊢
	proveit.numbers.ordering.relax_less
19	instantiation	33, 75	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
21	instantiation	34, 73, 94, 35*	⊢
	: , : , : , :
22	theorem		⊢
	proveit.logic.equality.equals_reversal
23	instantiation	36, 37	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.disassociation
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	76	⊢
	: , :
28	instantiation	95, 85, 45	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
30	instantiation	95, 85, 56	⊢
	: , : , :
31	instantiation	95, 85, 38	⊢
	: , : , :
32	instantiation	39	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
34	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
35	instantiation	59, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.elim_zero_left
37	instantiation	42, 43	⊢
	:
38	instantiation	44, 45, 56, 46	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	instantiation	67, 97, 47, 48, 49, 50	⊢
	: , : , : , :
41	instantiation	51, 52, 53	⊢
	:
42	theorem		⊢
	proveit.numbers.negation.complex_closure
43	instantiation	95, 85, 54	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
45	instantiation	55, 56	⊢
	:
46	instantiation	57, 58	⊢
	:
47	instantiation	76	⊢
	: , :
48	instantiation	76	⊢
	: , :
49	instantiation	59, 60, 61	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
51	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
52	instantiation	95, 85, 62	⊢
	: , : , :
53	instantiation	63, 64	⊢
	:
54	instantiation	95, 91, 65	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.negation.real_closure
56	instantiation	95, 91, 66	⊢
	: , : , :
57	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
58	assumption		⊢
59	axiom		⊢
	proveit.logic.equality.equals_transitivity
60	instantiation	67, 97, 68, 69, 70, 71	⊢
	: , : , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
62	instantiation	95, 91, 72	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
65	instantiation	95, 93, 73	⊢
	: , : , :
66	instantiation	95, 74, 75	⊢
	: , : , :
67	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
68	instantiation	76	⊢
	: , :
69	instantiation	76	⊢
	: , :
70	instantiation	77, 79	⊢
	:
71	instantiation	78, 79	⊢
	:
72	instantiation	95, 93, 80	⊢
	: , : , :
73	instantiation	95, 96, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
75	instantiation	82, 83, 84	⊢
	: , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
78	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
79	instantiation	95, 85, 86	⊢
	: , : , :
80	instantiation	95, 96, 87	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
82	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
83	instantiation	95, 89, 88	⊢
	: , : , :
84	instantiation	95, 89, 90	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	95, 91, 92	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
92	instantiation	95, 93, 94	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
94	instantiation	95, 96, 97	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
96	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements