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*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	38	⊢
3	reference	9	⊢
4	instantiation	47, 49, 92	⊢
	: , :
5	instantiation	8, 9, 49, 92, 10, 11	⊢
	: , : , :
6	instantiation	69, 12	⊢
	: , :
7	instantiation	26, 13, 14, 15	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.ordering.less_add_right
9	instantiation	57, 92, 17	⊢
	: , :
10	instantiation	16, 92, 17, 88, 18, 19	⊢
	: , : , :
11	instantiation	20, 115	⊢
	:
12	instantiation	26, 21, 22, 23	⊢
	: , : , : , :
13	instantiation	64, 72, 115, 105, 73, 25, 41, 86, 24	⊢
	: , : , : , : , : , :
14	instantiation	64, 115, 72, 25, 67, 73, 41, 86, 68, 75	⊢
	: , : , : , : , : , :
15	instantiation	26, 27, 28, 29	⊢
	: , : , : , :
16	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
18	instantiation	30, 31, 32	⊢
	: , : , :
19	instantiation	33, 34	⊢
	:
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
21	instantiation	35, 81, 85	⊢
	: , :
22	instantiation	36	⊢
	:
23	instantiation	69, 37	⊢
	: , :
24	instantiation	113, 91, 38	⊢
	: , : , :
25	instantiation	82	⊢
	: , :
26	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
27	instantiation	39, 105, 41, 86, 68, 75	⊢
	: , : , : , : , : , : , :
28	instantiation	43, 72, 115, 73, 40, 74, 41, 68, 86, 75, 42*	⊢
	: , : , : , : , : , :
29	instantiation	43, 105, 115, 72, 74, 73, 81, 86, 75, 77*	⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
31	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
32	instantiation	44, 103, 104, 101	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
35	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
36	axiom		⊢
	proveit.logic.equality.equals_reflexivity
37	instantiation	60, 45, 46	⊢
	: , : , :
38	instantiation	47, 48, 83	⊢
	: , :
39	theorem		⊢
	proveit.numbers.addition.leftward_commutation
40	instantiation	82	⊢
	: , :
41	instantiation	113, 91, 49	⊢
	: , : , :
42	instantiation	60, 50, 51, 52*	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.association
44	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
45	instantiation	76, 53	⊢
	: , : , :
46	instantiation	60, 54, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
48	instantiation	56, 88	⊢
	:
49	instantiation	57, 92, 88	⊢
	: , :
50	instantiation	76, 58	⊢
	: , : , :
51	instantiation	69, 59	⊢
	: , :
52	instantiation	60, 61, 62	⊢
	: , : , :
53	instantiation	63, 86	⊢
	:
54	instantiation	64, 105, 115, 72, 67, 73, 65, 68, 75	⊢
	: , : , : , : , : , :
55	instantiation	66, 72, 115, 73, 67, 68, 75	⊢
	: , : , : , :
56	theorem		⊢
	proveit.numbers.negation.real_closure
57	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
58	instantiation	69, 70	⊢
	: , :
59	instantiation	71, 72, 115, 105, 73, 74, 86, 75, 81	⊢
	: , : , : , : , : , :
60	axiom		⊢
	proveit.logic.equality.equals_transitivity
61	instantiation	76, 77	⊢
	: , : , :
62	instantiation	78, 81	⊢
	:
63	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
64	theorem		⊢
	proveit.numbers.addition.disassociation
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
66	theorem		⊢
	proveit.numbers.addition.elim_zero_any
67	instantiation	82	⊢
	: , :
68	instantiation	79, 81	⊢
	:
69	theorem		⊢
	proveit.logic.equality.equals_reversal
70	instantiation	80, 81	⊢
	:
71	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
72	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
73	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
74	instantiation	82	⊢
	: , :
75	instantiation	113, 91, 83	⊢
	: , : , :
76	axiom		⊢
	proveit.logic.equality.substitution
77	instantiation	84, 85, 86, 87	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
79	theorem		⊢
	proveit.numbers.negation.complex_closure
80	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
81	instantiation	113, 91, 88	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
83	instantiation	113, 96, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
85	instantiation	113, 91, 90	⊢
	: , : , :
86	instantiation	113, 91, 92	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
88	instantiation	113, 96, 93	⊢
	: , : , :
89	instantiation	113, 99, 94	⊢
	: , : , :
90	instantiation	113, 96, 95	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
92	instantiation	113, 96, 97	⊢
	: , : , :
93	instantiation	113, 99, 98	⊢
	: , : , :
94	instantiation	111, 103	⊢
	:
95	instantiation	113, 99, 103	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
97	instantiation	113, 99, 112	⊢
	: , : , :
98	instantiation	113, 100, 101	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
100	instantiation	102, 103, 104	⊢
	: , :
101	assumption		⊢
102	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
103	instantiation	113, 114, 105	⊢
	: , : , :
104	instantiation	106, 107, 108	⊢
	: , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
106	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
107	instantiation	113, 109, 110	⊢
	: , : , :
108	instantiation	111, 112	⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	instantiation	113, 114, 115	⊢
	: , : , :
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