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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
2	reference	7	⊢
3	instantiation	86, 76, 5	⊢
	: , : , :
4	instantiation	6, 7, 68, 33, 8, 9*, 10*, 11*	⊢
	: , : , : , :
5	instantiation	12, 77, 13, 38	⊢
	: , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
8	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
9	instantiation	44, 14, 15, 16	⊢
	: , : , : , :
10	instantiation	17, 29	⊢
	:
11	instantiation	80, 29	⊢
	:
12	theorem		⊢
	proveit.numbers.division.div_rational_closure
13	instantiation	86, 82, 18	⊢
	: , : , :
14	instantiation	19, 88, 26, 25, 20, 27, 29, 81, 30	⊢
	: , : , : , : , : , :
15	instantiation	65, 21, 22	⊢
	: , : , :
16	instantiation	72, 30	⊢
	:
17	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
18	instantiation	86, 23, 91	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.disassociation
20	instantiation	32	⊢
	: , :
21	instantiation	24, 25, 26, 88, 27, 28, 29, 81, 30	⊢
	: , : , : , : , : , :
22	instantiation	73, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
24	theorem		⊢
	proveit.numbers.multiplication.association
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	32	⊢
	: , :
29	instantiation	86, 84, 33	⊢
	: , : , :
30	instantiation	86, 84, 34	⊢
	: , : , :
31	instantiation	41, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	instantiation	37, 68, 85, 38	⊢
	: , :
34	instantiation	39, 40	⊢
	:
35	instantiation	41, 42, 43	⊢
	: , : , :
36	instantiation	44, 45, 46, 47	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.division.div_real_closure
38	instantiation	48, 91	⊢
	:
39	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
40	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	49, 60, 50, 51	⊢
	: , : , : , : , :
43	instantiation	65, 52, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
45	instantiation	73, 54	⊢
	: , : , :
46	instantiation	73, 54	⊢
	: , : , :
47	instantiation	80, 60	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
49	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
50	instantiation	86, 56, 55	⊢
	: , : , :
51	instantiation	86, 56, 57	⊢
	: , : , :
52	instantiation	73, 58	⊢
	: , : , :
53	instantiation	73, 59	⊢
	: , : , :
54	instantiation	75, 60	⊢
	:
55	instantiation	86, 62, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
57	instantiation	86, 62, 63	⊢
	: , : , :
58	instantiation	73, 64	⊢
	: , : , :
59	instantiation	65, 66, 67	⊢
	: , : , :
60	instantiation	86, 84, 68	⊢
	: , : , :
61	instantiation	86, 70, 69	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
63	instantiation	86, 70, 71	⊢
	: , : , :
64	instantiation	72, 81	⊢
	:
65	axiom		⊢
	proveit.logic.equality.equals_transitivity
66	instantiation	73, 74	⊢
	: , : , :
67	instantiation	75, 81	⊢
	:
68	instantiation	86, 76, 77	⊢
	: , : , :
69	instantiation	86, 79, 78	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
71	instantiation	86, 79, 91	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
73	axiom		⊢
	proveit.logic.equality.substitution
74	instantiation	80, 81	⊢
	:
75	theorem		⊢
	proveit.numbers.division.frac_one_denom
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
77	instantiation	86, 82, 83	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
81	instantiation	86, 84, 85	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	86, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	instantiation	89, 90, 91	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
89	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
90	instantiation	92, 93	⊢
	: , :
91	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
92	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements