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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	16, 6	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	modus ponens	7, 8	⊢
6	instantiation	9, 78, 10	⊢
	: , :
7	instantiation	11, 106	⊢
	: , : , : , : , : , : , :
8	generalization	12	⊢
9	modus ponens	13, 14	⊢
10	instantiation	127, 55, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
12	instantiation	16, 17	,  ⊢
	: , :
13	instantiation	18, 119, 106, 77	⊢
	: , : , : , : , : , :
14	generalization	19	⊢
15	instantiation	32, 38, 20, 21	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	22, 31, 23, 41, 24*	,  ⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
19	instantiation	127, 55, 25	,  ⊢
	: , : , :
20	instantiation	127, 65, 26	⊢
	: , : , :
21	instantiation	27, 50	⊢
	:
22	theorem		⊢
	proveit.numbers.division.prod_of_fracs
23	instantiation	127, 28, 29	⊢
	: , : , :
24	instantiation	30, 31	⊢
	:
25	instantiation	32, 38, 33, 34	,  ⊢
	: , :
26	instantiation	127, 72, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29	instantiation	127, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
31	instantiation	127, 55, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.division.div_real_closure
33	instantiation	39, 56, 129	,  ⊢
	: , :
34	instantiation	40, 41	,  ⊢
	:
35	instantiation	127, 128, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
37	instantiation	127, 43, 44	⊢
	: , : , :
38	instantiation	127, 65, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
41	instantiation	46, 47, 48	,  ⊢
	: , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
44	instantiation	127, 49, 50	⊢
	: , : , :
45	instantiation	127, 72, 116	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
47	instantiation	51, 52, 53	,  ⊢
	:
48	instantiation	127, 55, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
52	instantiation	127, 55, 56	,  ⊢
	: , : , :
53	instantiation	57, 58	,  ⊢
	: , :
54	instantiation	127, 65, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	60, 61, 62	,  ⊢
	: , :
57	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
58	instantiation	63, 64	,  ⊢
	: , :
59	instantiation	127, 72, 126	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
61	instantiation	127, 65, 66	,  ⊢
	: , : , :
62	instantiation	67, 68	⊢
	:
63	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
64	instantiation	69, 70, 80, 71	,  ⊢
	: , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	127, 72, 80	,  ⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.negation.real_closure
68	instantiation	73, 74, 75	⊢
	: , :
69	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
70	instantiation	76, 77, 119, 78	⊢
	: , : , : , : , :
71	instantiation	79, 80, 81, 82	,  ⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
73	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
74	instantiation	83, 84, 85	⊢
	: , : , :
75	instantiation	86, 87	⊢
	:
76	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
80	instantiation	127, 88, 97	,  ⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
82	instantiation	89, 90, 91	,  ⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
84	instantiation	92, 93	⊢
	: , :
85	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
86	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
87	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
88	instantiation	114, 95, 96	⊢
	: , :
89	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
90	instantiation	94, 95, 96, 97	,  ⊢
	: , : , :
91	instantiation	98, 99	⊢
	:
92	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
94	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
95	instantiation	120, 100, 116	⊢
	: , :
96	instantiation	125, 101	⊢
	:
97	assumption		⊢
98	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
99	instantiation	102, 103	⊢
	:
100	instantiation	125, 121	⊢
	:
101	instantiation	120, 108, 116	⊢
	: , :
102	theorem		⊢
	proveit.numbers.negation.int_neg_closure
103	instantiation	104, 105, 106	⊢
	: , :
104	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
105	instantiation	107, 108, 109	⊢
	:
106	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
107	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
108	instantiation	127, 110, 118	⊢
	: , : , :
109	instantiation	111, 112, 113	⊢
	: , : , :
110	instantiation	114, 116, 117	⊢
	: , :
111	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
112	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
113	instantiation	115, 116, 117, 118	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
115	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
116	instantiation	127, 128, 119	⊢
	: , : , :
117	instantiation	120, 121, 122	⊢
	: , :
118	assumption		⊢
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
120	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
121	instantiation	127, 123, 124	⊢
	: , : , :
122	instantiation	125, 126	⊢
	:
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
124	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
125	theorem		⊢
	proveit.numbers.negation.int_closure
126	instantiation	127, 128, 129	⊢
	: , : , :
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements