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