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*, 8*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound
2	instantiation	9, 36	⊢
	:
3	instantiation	10, 12, 36, 13	⊢
	: , : , :
4	reference	36	⊢
5	instantiation	11, 12, 36, 13	⊢
	: , : , :
6	instantiation	14, 15	⊢
	:
7	instantiation	16, 29, 17*	⊢
	: , :
8	instantiation	18, 19, 20	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.negation.real_closure
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
13	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
14	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
15	instantiation	21, 22	⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
17	instantiation	23, 29	⊢
	:
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	24, 54, 61, 31, 33, 32, 25, 34, 35	⊢
	: , : , : , : , : , :
20	instantiation	26, 31, 61, 32, 33, 29, 34, 35, 27*	⊢
	: , : , : , : , :
21	theorem		⊢
	proveit.numbers.negation.int_neg_closure
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
23	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
24	theorem		⊢
	proveit.numbers.multiplication.disassociation
25	instantiation	28, 29	⊢
	:
26	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
27	instantiation	30, 31, 61, 32, 33, 34, 35	⊢
	: , : , : , :
28	theorem		⊢
	proveit.numbers.negation.complex_closure
29	instantiation	59, 44, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	37	⊢
	: , :
34	instantiation	38, 39, 40	⊢
	: , :
35	instantiation	59, 44, 41	⊢
	: , : , :
36	instantiation	59, 49, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
39	instantiation	59, 44, 43	⊢
	: , : , :
40	instantiation	59, 44, 45	⊢
	: , : , :
41	instantiation	46, 47	⊢
	:
42	instantiation	59, 55, 48	⊢
	: , : , :
43	instantiation	59, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	51, 52, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
47	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
48	instantiation	59, 60, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	59, 55, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
52	instantiation	57, 58	⊢
	: , :
53	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	59, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements