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	reference	5	⊢
2	instantiation	34, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 16, 8*	⊢
	:
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	9, 10	⊢
	:
7	theorem		⊢
	proveit.numbers.absolute_value.abs_even
8	instantiation	11, 12, 13, 51, 52, 73, 53, 14*	⊢
	: , :
9	theorem		⊢
	proveit.numbers.addition.elim_zero_left
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
13	instantiation	17	⊢
	: , : , : , :
14	instantiation	34, 18, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.negation.complex_closure
16	instantiation	20, 21, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
18	instantiation	23, 30, 24, 25, 26, 27, 28	⊢
	: , : , : , :
19	instantiation	29, 47, 30, 48, 31, 51, 52, 32, 53	⊢
	: , : , : , : , : , : , :
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	instantiation	87, 81, 33	⊢
	: , : , :
22	instantiation	34, 35, 36	⊢
	: , : , :
23	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
24	instantiation	41	⊢
	: , : , :
25	instantiation	41	⊢
	: , : , :
26	instantiation	39, 37	⊢
	:
27	instantiation	39, 38	⊢
	:
28	instantiation	39, 40	⊢
	:
29	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
31	instantiation	41	⊢
	: , : , :
32	instantiation	87, 81, 42	⊢
	: , : , :
33	instantiation	66, 59, 43	⊢
	: , :
34	axiom		⊢
	proveit.logic.equality.equals_transitivity
35	instantiation	46, 44, 89, 47, 50, 48, 45, 73, 53	⊢
	: , : , : , : , : , :
36	instantiation	46, 47, 89, 48, 49, 50, 51, 52, 73, 53	⊢
	: , : , : , : , : , :
37	instantiation	54, 89	⊢
	:
38	instantiation	56, 55	⊢
	: , :
39	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
40	instantiation	56, 57	⊢
	: , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
42	instantiation	87, 77, 58	⊢
	: , : , :
43	instantiation	66, 82, 61	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
45	instantiation	87, 81, 59	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.multiplication.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	60	⊢
	: , :
50	instantiation	60	⊢
	: , :
51	instantiation	87, 81, 67	⊢
	: , : , :
52	instantiation	87, 81, 68	⊢
	: , : , :
53	instantiation	87, 81, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
55	instantiation	62, 78	⊢
	:
56	theorem		⊢
	proveit.numbers.ordering.relax_less
57	instantiation	63, 71	⊢
	:
58	instantiation	64, 65	⊢
	:
59	instantiation	66, 67, 68	⊢
	: , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	instantiation	69, 70, 71	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
64	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
65	instantiation	72, 73, 74	⊢
	:
66	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
67	instantiation	87, 75, 76	⊢
	: , : , :
68	instantiation	87, 77, 78	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
70	instantiation	79, 80	⊢
	: , :
71	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
73	instantiation	87, 81, 82	⊢
	: , : , :
74	assumption		⊢
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	87, 83, 84	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
79	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
82	instantiation	85, 86	⊢
	:
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	instantiation	87, 88, 89	⊢
	: , : , :
85	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
86	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
87	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements