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.division.weak_div_from_numer_bound__pos_denom
2	reference	36	⊢
3	reference	45	⊢
4	instantiation	59, 19, 18	⊢
	: , :
5	instantiation	8, 9, 10	⊢
	: , : , :
6	instantiation	11, 46	⊢
	:
7	instantiation	12, 52, 22, 23, 13*	⊢
	: , :
8	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
9	instantiation	14, 34, 45, 18, 15, 16*	⊢
	: , : , :
10	instantiation	17, 18, 34, 19, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
12	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
13	instantiation	21, 52, 22, 23, 24*	⊢
	: , :
14	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
15	instantiation	25, 102, 63, 62, 26, 27, 28*, 29*	⊢
	: , : , :
16	instantiation	30, 31	⊢
	:
17	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
18	instantiation	110, 63	⊢
	:
19	instantiation	32, 34, 74, 35	⊢
	: , : , :
20	instantiation	33, 34, 74, 35	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.div_as_mult
22	instantiation	135, 101, 36	⊢
	: , : , :
23	instantiation	64, 46	⊢
	:
24	instantiation	76, 37, 38	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
26	instantiation	39, 109, 128, 98	⊢
	: , : , :
27	instantiation	40, 41	⊢
	: , :
28	instantiation	43, 66, 52, 42*	⊢
	: , :
29	instantiation	43, 66, 54, 44*	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.elim_zero_left
31	instantiation	135, 101, 45	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
36	instantiation	121, 122, 46	⊢
	: , : , :
37	instantiation	68, 47	⊢
	: , : , :
38	instantiation	48, 82, 49, 100, 57, 50*	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
40	theorem		⊢
	proveit.numbers.ordering.relax_less
41	instantiation	51, 134	⊢
	:
42	instantiation	53, 52	⊢
	:
43	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
44	instantiation	53, 54	⊢
	:
45	instantiation	135, 106, 55	⊢
	: , : , :
46	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47	instantiation	56, 82, 111, 102, 57, 58*	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
49	instantiation	59, 111, 102	⊢
	: , :
50	instantiation	76, 60, 61	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
52	instantiation	135, 101, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
54	instantiation	135, 101, 63	⊢
	: , : , :
55	instantiation	135, 116, 119	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
57	instantiation	64, 115	⊢
	:
58	instantiation	65, 91, 66, 67*	⊢
	: , :
59	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
60	instantiation	68, 69	⊢
	: , : , :
61	instantiation	70, 71, 139, 72*	⊢
	: , :
62	instantiation	121, 122, 137	⊢
	: , : , :
63	instantiation	135, 106, 73	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
65	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
66	instantiation	135, 101, 74	⊢
	: , : , :
67	instantiation	75, 91	⊢
	:
68	axiom		⊢
	proveit.logic.equality.substitution
69	instantiation	76, 77, 78	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
71	instantiation	135, 79, 80	⊢
	: , : , :
72	instantiation	81, 82	⊢
	:
73	instantiation	135, 116, 83	⊢
	: , : , :
74	instantiation	135, 106, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
76	axiom		⊢
	proveit.logic.equality.equals_transitivity
77	instantiation	85, 86, 126, 130, 87, 88, 91, 92, 89	⊢
	: , : , : , : , : , :
78	instantiation	90, 91, 92, 93	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
80	instantiation	135, 94, 95	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
82	instantiation	135, 101, 96	⊢
	: , : , :
83	instantiation	135, 97, 98	⊢
	: , : , :
84	instantiation	135, 116, 120	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.addition.disassociation
86	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
87	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
88	instantiation	99	⊢
	: , :
89	instantiation	135, 101, 100	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
91	instantiation	135, 101, 111	⊢
	: , : , :
92	instantiation	135, 101, 102	⊢
	: , : , :
93	instantiation	103	⊢
	:
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
95	instantiation	135, 104, 105	⊢
	: , : , :
96	instantiation	135, 106, 107	⊢
	: , : , :
97	instantiation	108, 109, 128	⊢
	: , :
98	assumption		⊢
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
100	instantiation	110, 111	⊢
	:
101	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
102	instantiation	135, 112, 113	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.equals_reflexivity
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
105	instantiation	135, 114, 115	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
107	instantiation	135, 116, 117	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
109	instantiation	118, 119, 120	⊢
	: , :
110	theorem		⊢
	proveit.numbers.negation.real_closure
111	instantiation	121, 122, 123	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
113	instantiation	135, 124, 125	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
117	instantiation	135, 129, 126	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
119	instantiation	127, 128	⊢
	:
120	instantiation	135, 129, 130	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
122	instantiation	131, 132	⊢
	: , :
123	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
125	instantiation	135, 133, 134	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	instantiation	135, 136, 137	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
131	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
134	instantiation	138, 139	⊢
	:
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
137	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
138	theorem		⊢
	proveit.numbers.negation.int_neg_closure
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements