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.booleans.conjunction.and_if_both
2	instantiation	4, 92, 101, 89	⊢
	: , : , :
3	instantiation	5, 66, 80, 6, 7, 8*, 9*	, ,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
5	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
6	instantiation	10, 11, 13	, ,  ⊢
	: , : , :
7	instantiation	12, 13	, ,  ⊢
	:
8	instantiation	34, 14, 15	⊢
	: , : , :
9	instantiation	29, 16	,  ⊢
	: , :
10	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
11	instantiation	17, 18	⊢
	: , :
12	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
13	instantiation	19, 20	, ,  ⊢
	:
14	instantiation	54, 102, 109, 59, 56, 60, 71, 62, 63	⊢
	: , : , : , : , : , :
15	instantiation	21, 71, 62, 22	⊢
	: , : , :
16	instantiation	44, 23, 24, 25	,  ⊢
	: , : , : , :
17	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
19	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
20	instantiation	26, 27, 28	, ,  ⊢
	:
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
22	instantiation	51	⊢
	:
23	instantiation	52, 69, 71	⊢
	: , :
24	instantiation	51	⊢
	:
25	instantiation	29, 30	,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
27	instantiation	99, 86, 85	,  ⊢
	: , :
28	instantiation	31, 76, 77, 68, 32, 33*	, ,  ⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.equals_reversal
30	instantiation	34, 35, 36	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
32	instantiation	37, 38, 39	,  ⊢
	: , : , :
33	instantiation	40, 62, 41	⊢
	: , :
34	axiom		⊢
	proveit.logic.equality.equals_transitivity
35	instantiation	42, 43	,  ⊢
	: , : , :
36	instantiation	44, 45, 46, 47	,  ⊢
	: , : , : , :
37	theorem		⊢
	proveit.logic.equality.sub_right_side_into
38	instantiation	48, 94	⊢
	: , :
39	instantiation	49, 89, 50*	,  ⊢
	:
40	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
41	instantiation	51	⊢
	:
42	axiom		⊢
	proveit.logic.equality.substitution
43	instantiation	52, 69, 62	,  ⊢
	: , :
44	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
45	instantiation	54, 59, 109, 102, 60, 55, 61, 57, 53	,  ⊢
	: , : , : , : , : , :
46	instantiation	54, 109, 59, 55, 56, 60, 61, 57, 62, 63	,  ⊢
	: , : , : , : , : , :
47	instantiation	58, 102, 59, 60, 61, 62, 63	,  ⊢
	: , : , : , : , : , : , : , :
48	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
49	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
50	instantiation	64, 65	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
53	instantiation	107, 78, 66	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.disassociation
55	instantiation	67	⊢
	: , :
56	instantiation	67	⊢
	: , :
57	instantiation	107, 78, 68	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
59	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
60	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
61	instantiation	70, 69	⊢
	:
62	instantiation	107, 78, 76	⊢
	: , : , :
63	instantiation	70, 71	⊢
	:
64	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
65	instantiation	72, 73	⊢
	: , :
66	instantiation	74, 76, 75	⊢
	: , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	instantiation	79, 76	⊢
	:
69	instantiation	107, 78, 77	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.negation.complex_closure
71	instantiation	107, 78, 80	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.ordering.relax_less
73	assumption		⊢
74	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
75	instantiation	79, 80	⊢
	:
76	instantiation	107, 83, 81	⊢
	: , : , :
77	instantiation	107, 83, 82	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	theorem		⊢
	proveit.numbers.negation.real_closure
80	instantiation	107, 83, 84	⊢
	: , : , :
81	instantiation	107, 87, 85	⊢
	: , : , :
82	instantiation	107, 87, 86	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
84	instantiation	107, 87, 98	⊢
	: , : , :
85	instantiation	107, 88, 89	⊢
	: , : , :
86	instantiation	107, 90, 91	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
88	instantiation	95, 92, 101	⊢
	: , :
89	instantiation	93, 94	⊢
	: , :
90	instantiation	95, 98, 96	⊢
	: , :
91	assumption		⊢
92	instantiation	99, 97, 98	⊢
	: , :
93	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
96	instantiation	99, 101, 100	⊢
	: , :
97	instantiation	103, 101	⊢
	:
98	instantiation	107, 108, 102	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
100	instantiation	103, 104	⊢
	:
101	instantiation	107, 105, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
103	theorem		⊢
	proveit.numbers.negation.int_closure
104	instantiation	107, 108, 109	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
106	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements