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	generalization	1	⊢
1	instantiation	2, 3, 4, 5, 6	,  ⊢
	: , : , :
2	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
3	instantiation	125, 7, 8	⊢
	: , : , :
4	instantiation	10, 55, 9	,  ⊢
	:
5	instantiation	10, 19, 11	,  ⊢
	:
6	instantiation	12, 90, 19, 55, 13, 14	,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
8	instantiation	125, 15, 117	⊢
	: , : , :
9	instantiation	16, 75, 17, 31	,  ⊢
	: , :
10	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
11	instantiation	18, 19, 47, 20	,  ⊢
	: , :
12	theorem		⊢
	proveit.numbers.exponentiation.exp_even_neg_base_lesseq
13	instantiation	21, 22, 31	,  ⊢
	: , :
14	instantiation	23	⊢
	:
15	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
16	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
17	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
18	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
19	instantiation	24, 55, 28	,  ⊢
	: , :
20	instantiation	25, 26	,  ⊢
	: , :
21	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
22	instantiation	27, 55, 28, 47, 29, 30*	,  ⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
26	instantiation	97, 31, 35	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
28	instantiation	44, 34	⊢
	:
29	instantiation	32, 33, 47, 34, 35, 36, 37*, 38*	⊢
	: , : , :
30	instantiation	39, 40	,  ⊢
	:
31	instantiation	41, 42, 43	,  ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
33	instantiation	44, 79	⊢
	:
34	instantiation	45, 47, 79, 48	⊢
	: , : , :
35	instantiation	46, 47, 79, 48	⊢
	: , : , :
36	instantiation	49, 50	⊢
	: , :
37	instantiation	51, 52, 53	⊢
	: , : , :
38	instantiation	54, 61	⊢
	:
39	theorem		⊢
	proveit.numbers.addition.elim_zero_right
40	instantiation	125, 91, 55	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
42	instantiation	56, 95, 96, 86	,  ⊢
	: , : , :
43	instantiation	58, 57	⊢
	:
44	theorem		⊢
	proveit.numbers.negation.real_closure
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
48	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
49	theorem		⊢
	proveit.numbers.ordering.relax_less
50	instantiation	58, 59	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_transitivity
52	instantiation	60, 117, 127, 70, 72, 71, 61, 73, 74	⊢
	: , : , : , : , : , :
53	instantiation	62, 70, 127, 71, 72, 68, 73, 74, 63*	⊢
	: , : , : , : , :
54	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
55	instantiation	125, 100, 64	,  ⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
57	instantiation	66, 65	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
59	instantiation	66, 78	⊢
	:
60	theorem		⊢
	proveit.numbers.multiplication.disassociation
61	instantiation	67, 68	⊢
	:
62	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
63	instantiation	69, 70, 127, 71, 72, 73, 74	⊢
	: , : , : , :
64	instantiation	125, 108, 75	,  ⊢
	: , : , :
65	instantiation	76, 77, 78	⊢
	: , :
66	theorem		⊢
	proveit.numbers.negation.int_neg_closure
67	theorem		⊢
	proveit.numbers.negation.complex_closure
68	instantiation	125, 91, 79	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
70	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
71	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
72	instantiation	80	⊢
	: , :
73	instantiation	81, 82, 83	⊢
	: , :
74	instantiation	125, 91, 84	⊢
	: , : , :
75	instantiation	125, 85, 86	,  ⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
77	instantiation	87, 111, 88	⊢
	:
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	instantiation	125, 100, 89	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
81	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
82	instantiation	125, 91, 90	⊢
	: , : , :
83	instantiation	125, 91, 92	⊢
	: , : , :
84	instantiation	93, 94	⊢
	:
85	instantiation	114, 95, 96	⊢
	: , :
86	assumption		⊢
87	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
88	instantiation	97, 98, 99	⊢
	: , : , :
89	instantiation	125, 108, 115	⊢
	: , : , :
90	instantiation	125, 100, 101	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
92	instantiation	102, 103, 104	⊢
	: , : , :
93	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
94	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
95	instantiation	118, 105, 115	⊢
	: , :
96	instantiation	123, 106	⊢
	:
97	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
98	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
99	instantiation	107, 115, 116, 113	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
101	instantiation	125, 108, 124	⊢
	: , : , :
102	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
103	instantiation	109, 110	⊢
	: , :
104	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
105	instantiation	123, 119	⊢
	:
106	instantiation	118, 111, 115	⊢
	: , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
109	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
111	instantiation	125, 112, 113	⊢
	: , : , :
112	instantiation	114, 115, 116	⊢
	: , :
113	assumption		⊢
114	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
115	instantiation	125, 126, 117	⊢
	: , : , :
116	instantiation	118, 119, 120	⊢
	: , :
117	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
118	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
119	instantiation	125, 121, 122	⊢
	: , : , :
120	instantiation	123, 124	⊢
	:
121	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
122	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
123	theorem		⊢
	proveit.numbers.negation.int_closure
124	instantiation	125, 126, 127	⊢
	: , : , :
125	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements