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