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