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	instantiation	8, 61, 9	,  ⊢
	: , :
3	reference	50	,  ⊢
4	instantiation	87, 64, 10	⊢
	: , : , :
5	instantiation	11, 50, 12, 53, 13, 14	,  ⊢
	: , : , :
6	instantiation	36, 15, 16	,  ⊢
	: , : , :
7	instantiation	36, 17, 18	,  ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	instantiation	19, 50	,  ⊢
	:
10	instantiation	87, 68, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
12	instantiation	87, 64, 21	⊢
	: , : , :
13	instantiation	22, 69, 70, 67	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
15	instantiation	41, 79, 89, 42, 30, 43, 39, 55, 32	,  ⊢
	: , : , : , : , : , :
16	instantiation	23, 39, 55, 24	,  ⊢
	: , : , :
17	instantiation	34, 25	⊢
	: , : , :
18	instantiation	36, 26, 27	,  ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.negation.real_closure
20	instantiation	80, 70, 77	⊢
	: , :
21	instantiation	87, 68, 70	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
23	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
24	instantiation	56	⊢
	:
25	instantiation	36, 28, 29	⊢
	: , : , :
26	instantiation	41, 79, 89, 42, 30, 43, 48, 55, 32	,  ⊢
	: , : , : , : , : , :
27	instantiation	31, 55, 32, 33	,  ⊢
	: , : , :
28	instantiation	34, 35	⊢
	: , : , :
29	instantiation	36, 37, 38	⊢
	: , : , :
30	instantiation	51	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_21
32	instantiation	54, 39	,  ⊢
	:
33	instantiation	56	⊢
	:
34	axiom		⊢
	proveit.logic.equality.substitution
35	instantiation	40, 55, 47	⊢
	: , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	41, 42, 89, 79, 43, 44, 48, 45, 47	⊢
	: , : , : , : , : , :
38	instantiation	46, 47, 48, 49	⊢
	: , : , :
39	instantiation	87, 60, 50	,  ⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
41	theorem		⊢
	proveit.numbers.addition.disassociation
42	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
43	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
44	instantiation	51	⊢
	: , :
45	instantiation	87, 60, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
47	instantiation	87, 60, 53	⊢
	: , : , :
48	instantiation	54, 55	⊢
	:
49	instantiation	56	⊢
	:
50	instantiation	87, 64, 57	,  ⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	instantiation	87, 64, 58	⊢
	: , : , :
53	instantiation	87, 64, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.negation.complex_closure
55	instantiation	87, 60, 61	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.equals_reflexivity
57	instantiation	87, 68, 62	,  ⊢
	: , : , :
58	instantiation	87, 68, 63	⊢
	: , : , :
59	instantiation	87, 68, 77	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	87, 64, 65	⊢
	: , : , :
62	instantiation	87, 66, 67	,  ⊢
	: , : , :
63	instantiation	85, 77	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	87, 68, 73	⊢
	: , : , :
66	instantiation	76, 69, 70	⊢
	: , :
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	80, 71, 77	⊢
	: , :
70	instantiation	85, 72	⊢
	:
71	instantiation	85, 81	⊢
	:
72	instantiation	80, 73, 77	⊢
	: , :
73	instantiation	87, 74, 75	⊢
	: , : , :
74	instantiation	76, 77, 78	⊢
	: , :
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
77	instantiation	87, 88, 79	⊢
	: , : , :
78	instantiation	80, 81, 82	⊢
	: , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
80	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
81	instantiation	87, 83, 84	⊢
	: , : , :
82	instantiation	85, 86	⊢
	:
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
84	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
85	theorem		⊢
	proveit.numbers.negation.int_closure
86	instantiation	87, 88, 89	⊢
	: , : , :
87	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements