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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 33, 5, 53, 6, 7, 8*, 9*	⊢
	: , : , :
3	instantiation	10, 17, 77, 19, 29, 22, 20	⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
5	instantiation	11, 37, 32	⊢
	: , :
6	instantiation	12, 13, 14	⊢
	: , : , :
7	instantiation	48, 15	⊢
	: , :
8	instantiation	16, 77, 80, 17, 18, 19, 22, 29, 20	⊢
	: , : , : , : , : , :
9	instantiation	21, 22, 23	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
11	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
12	theorem		⊢
	proveit.logic.equality.sub_right_side_into
13	instantiation	24, 25, 26	⊢
	: , :
14	instantiation	27, 71, 28, 29, 59, 30*	⊢
	: , :
15	instantiation	31, 42	⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.disassociation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	instantiation	36	⊢
	: , :
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	78, 65, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.commutation
22	instantiation	78, 65, 33	⊢
	: , : , :
23	instantiation	78, 65, 53	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
25	instantiation	34, 44, 53, 45	⊢
	: , : , :
26	instantiation	48, 35	⊢
	: , :
27	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
28	instantiation	36	⊢
	: , :
29	instantiation	78, 65, 37	⊢
	: , : , :
30	instantiation	38, 39	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
32	instantiation	78, 41, 40	⊢
	: , : , :
33	instantiation	78, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
35	instantiation	43, 44, 53, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	instantiation	46, 47, 57	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
39	instantiation	48, 49	⊢
	: , :
40	instantiation	50, 51	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
44	instantiation	52, 53	⊢
	:
45	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	54, 55	⊢
	: , :
48	theorem		⊢
	proveit.numbers.ordering.relax_less
49	instantiation	56, 57	⊢
	:
50	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
51	instantiation	58, 59, 60	⊢
	:
52	theorem		⊢
	proveit.numbers.negation.real_closure
53	instantiation	61, 62, 63, 64	⊢
	: , :
54	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
57	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
59	instantiation	78, 65, 66	⊢
	: , : , :
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.division.div_real_closure
62	instantiation	78, 68, 67	⊢
	: , : , :
63	instantiation	78, 68, 69	⊢
	: , : , :
64	instantiation	70, 71	⊢
	:
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	instantiation	72, 73	⊢
	:
67	instantiation	78, 75, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	78, 75, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
72	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
73	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
74	instantiation	78, 79, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	78, 79, 80	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
78	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements