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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
2	reference	16	⊢
3	reference	48	⊢
4	instantiation	100, 90, 7	⊢
	: , : , :
5	instantiation	8, 16, 9, 10	⊢
	: , : , :
6	instantiation	11, 13	⊢
	:
7	instantiation	100, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
9	instantiation	100, 90, 14	⊢
	: , : , :
10	instantiation	15, 16, 82, 47, 17, 18*, 19*, 20*	⊢
	: , : , : , :
11	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
12	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
13	instantiation	21, 22, 23	⊢
	: , :
14	instantiation	24, 91, 25, 52	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
18	instantiation	58, 26, 27, 28	⊢
	: , : , : , :
19	instantiation	29, 43	⊢
	:
20	instantiation	94, 43	⊢
	:
21	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
22	instantiation	100, 30, 92	⊢
	: , : , :
23	instantiation	100, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.div_rational_closure
25	instantiation	100, 96, 32	⊢
	: , : , :
26	instantiation	33, 102, 40, 39, 34, 41, 43, 95, 44	⊢
	: , : , : , : , : , :
27	instantiation	79, 35, 36	⊢
	: , : , :
28	instantiation	86, 44	⊢
	:
29	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
32	instantiation	100, 37, 105	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.disassociation
34	instantiation	46	⊢
	: , :
35	instantiation	38, 39, 40, 102, 41, 42, 43, 95, 44	⊢
	: , : , : , : , : , :
36	instantiation	87, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
38	theorem		⊢
	proveit.numbers.multiplication.association
39	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42	instantiation	46	⊢
	: , :
43	instantiation	100, 98, 47	⊢
	: , : , :
44	instantiation	100, 98, 48	⊢
	: , : , :
45	instantiation	55, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	instantiation	51, 82, 99, 52	⊢
	: , :
48	instantiation	53, 54	⊢
	:
49	instantiation	55, 56, 57	⊢
	: , : , :
50	instantiation	58, 59, 60, 61	⊢
	: , : , : , :
51	theorem		⊢
	proveit.numbers.division.div_real_closure
52	instantiation	62, 105	⊢
	:
53	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
54	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
55	theorem		⊢
	proveit.logic.equality.sub_right_side_into
56	instantiation	63, 74, 64, 65	⊢
	: , : , : , : , :
57	instantiation	79, 66, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
59	instantiation	87, 68	⊢
	: , : , :
60	instantiation	87, 68	⊢
	: , : , :
61	instantiation	94, 74	⊢
	:
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
63	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
64	instantiation	100, 70, 69	⊢
	: , : , :
65	instantiation	100, 70, 71	⊢
	: , : , :
66	instantiation	87, 72	⊢
	: , : , :
67	instantiation	87, 73	⊢
	: , : , :
68	instantiation	89, 74	⊢
	:
69	instantiation	100, 76, 75	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
71	instantiation	100, 76, 77	⊢
	: , : , :
72	instantiation	87, 78	⊢
	: , : , :
73	instantiation	79, 80, 81	⊢
	: , : , :
74	instantiation	100, 98, 82	⊢
	: , : , :
75	instantiation	100, 84, 83	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
77	instantiation	100, 84, 85	⊢
	: , : , :
78	instantiation	86, 95	⊢
	:
79	axiom		⊢
	proveit.logic.equality.equals_transitivity
80	instantiation	87, 88	⊢
	: , : , :
81	instantiation	89, 95	⊢
	:
82	instantiation	100, 90, 91	⊢
	: , : , :
83	instantiation	100, 93, 92	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
85	instantiation	100, 93, 105	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
87	axiom		⊢
	proveit.logic.equality.substitution
88	instantiation	94, 95	⊢
	:
89	theorem		⊢
	proveit.numbers.division.frac_one_denom
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
91	instantiation	100, 96, 97	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
94	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
95	instantiation	100, 98, 99	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
97	instantiation	100, 101, 102	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
99	instantiation	103, 104, 105	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
103	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
104	instantiation	106, 107	⊢
	: , :
105	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
106	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements