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	modus ponens	1, 2	⊢
1	instantiation	3	⊢
	: , : , :
2	generalization	4	⊢
3	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
4	instantiation	48, 5	,  ⊢
	: , :
5	instantiation	6, 7, 8, 9, 10	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
7	instantiation	139, 12, 11	⊢
	: , : , :
8	instantiation	139, 12, 13	,  ⊢
	: , : , :
9	instantiation	14, 31, 15	,  ⊢
	:
10	instantiation	16, 105, 17, 31, 18, 19	,  ⊢
	: , : , :
11	instantiation	139, 20, 75	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
13	instantiation	139, 20, 21	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
15	instantiation	22, 23	,  ⊢
	: , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
17	instantiation	38, 39, 43	,  ⊢
	: , :
18	instantiation	24, 37, 25	,  ⊢
	: , :
19	instantiation	26, 27	⊢
	:
20	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
21	instantiation	28, 29, 141	,  ⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
23	instantiation	30, 87, 31, 32	,  ⊢
	: , :
24	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
25	instantiation	33, 39, 43, 40, 34	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
29	instantiation	35, 36, 37	,  ⊢
	:
30	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
31	instantiation	38, 39, 40	,  ⊢
	: , :
32	instantiation	63, 41	,  ⊢
	: , :
33	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
34	instantiation	42, 43, 51, 122, 53, 44, 45*, 46*	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
36	instantiation	129, 65, 47	,  ⊢
	: , :
37	instantiation	48, 49	,  ⊢
	: , :
38	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
39	instantiation	139, 127, 50	,  ⊢
	: , : , :
40	instantiation	54, 51	⊢
	:
41	instantiation	52, 53, 64	,  ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound
43	instantiation	54, 122	⊢
	:
44	instantiation	55, 62	⊢
	:
45	instantiation	56, 113, 57*	⊢
	: , :
46	instantiation	58, 59, 60	⊢
	: , : , :
47	instantiation	139, 61, 62	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.ordering.relax_less
49	instantiation	63, 64	,  ⊢
	: , :
50	instantiation	139, 132, 65	,  ⊢
	: , : , :
51	instantiation	66, 87, 122, 68	⊢
	: , : , :
52	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
53	instantiation	67, 87, 122, 68	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.negation.real_closure
55	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
56	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
57	instantiation	69, 113	⊢
	:
58	axiom		⊢
	proveit.logic.equality.equals_transitivity
59	instantiation	70, 138, 141, 81, 83, 82, 71, 84, 85	⊢
	: , : , : , : , : , :
60	instantiation	72, 81, 141, 82, 83, 113, 84, 85, 73*	⊢
	: , : , : , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
62	instantiation	74, 75	⊢
	:
63	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
64	instantiation	99, 76, 77	,  ⊢
	: , : , :
65	instantiation	139, 78, 91	,  ⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
68	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
69	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
70	theorem		⊢
	proveit.numbers.multiplication.disassociation
71	instantiation	79, 113	⊢
	:
72	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
73	instantiation	80, 81, 141, 82, 83, 84, 85	⊢
	: , : , : , :
74	theorem		⊢
	proveit.numbers.negation.int_neg_closure
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
76	instantiation	86, 122, 87, 88, 89, 90*	⊢
	: , : , :
77	instantiation	110, 92, 130, 91	,  ⊢
	: , : , :
78	instantiation	125, 92, 130	⊢
	: , :
79	theorem		⊢
	proveit.numbers.negation.complex_closure
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
81	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
82	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
83	instantiation	93	⊢
	: , :
84	instantiation	94, 95, 96	⊢
	: , :
85	instantiation	139, 121, 97	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
88	instantiation	139, 127, 98	⊢
	: , : , :
89	instantiation	99, 100, 101	⊢
	: , : , :
90	instantiation	102, 103, 104	⊢
	: , : , :
91	assumption		⊢
92	instantiation	129, 109, 133	⊢
	: , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
94	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
95	instantiation	139, 121, 105	⊢
	: , : , :
96	instantiation	139, 121, 106	⊢
	: , : , :
97	instantiation	107, 108	⊢
	:
98	instantiation	139, 132, 109	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
100	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
101	instantiation	110, 133, 126, 120	⊢
	: , : , :
102	theorem		⊢
	proveit.logic.equality.sub_right_side_into
103	instantiation	111, 113	⊢
	:
104	instantiation	112, 113, 114	⊢
	: , :
105	instantiation	139, 127, 115	⊢
	: , : , :
106	instantiation	116, 117, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
108	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
109	instantiation	139, 119, 120	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
111	theorem		⊢
	proveit.numbers.addition.elim_zero_right
112	theorem		⊢
	proveit.numbers.addition.commutation
113	instantiation	139, 121, 122	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
115	instantiation	139, 132, 137	⊢
	: , : , :
116	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
117	instantiation	123, 124	⊢
	: , :
118	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
119	instantiation	125, 133, 126	⊢
	: , :
120	assumption		⊢
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	139, 127, 128	⊢
	: , : , :
123	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
125	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
126	instantiation	129, 130, 131	⊢
	: , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
128	instantiation	139, 132, 133	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
130	instantiation	139, 134, 135	⊢
	: , : , :
131	instantiation	136, 137	⊢
	:
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	instantiation	139, 140, 138	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
135	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
136	theorem		⊢
	proveit.numbers.negation.int_closure
137	instantiation	139, 140, 141	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
139	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements