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	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 31, 57, 85, 8*	⊢
	: , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	9, 46, 10, 72, 11, 12, 13*, 17*	⊢
	: , : , :
6	instantiation	14, 24, 99, 26, 38, 31, 27	⊢
	: , : , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.division.div_as_mult
8	instantiation	15, 16, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
10	instantiation	18, 50, 41	⊢
	: , :
11	instantiation	19, 20, 21	⊢
	: , : , :
12	instantiation	65, 22	⊢
	: , :
13	instantiation	23, 99, 102, 24, 25, 26, 31, 38, 27	⊢
	: , : , : , : , : , :
14	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	28, 29	⊢
	: , : , :
17	instantiation	30, 31, 32	⊢
	: , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	33, 34, 35	⊢
	: , :
21	instantiation	36, 93, 37, 38, 78, 39*	⊢
	: , :
22	instantiation	40, 59	⊢
	:
23	theorem		⊢
	proveit.numbers.multiplication.disassociation
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	instantiation	49	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	100, 86, 41	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.substitution
29	instantiation	42, 43, 44, 45*	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.commutation
31	instantiation	100, 86, 46	⊢
	: , : , :
32	instantiation	100, 86, 72	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
34	instantiation	47, 61, 72, 62	⊢
	: , : , :
35	instantiation	65, 48	⊢
	: , :
36	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
37	instantiation	49	⊢
	: , :
38	instantiation	100, 86, 50	⊢
	: , : , :
39	instantiation	51, 52	⊢
	:
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
41	instantiation	100, 58, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
43	instantiation	100, 54, 55	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	instantiation	56, 57	⊢
	:
46	instantiation	100, 58, 59	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
48	instantiation	60, 61, 72, 62	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	instantiation	63, 64, 76	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
52	instantiation	65, 66	⊢
	: , :
53	instantiation	67, 68	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55	instantiation	100, 69, 70	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
57	instantiation	100, 86, 84	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
61	instantiation	71, 72	⊢
	:
62	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
63	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
64	instantiation	73, 74	⊢
	: , :
65	theorem		⊢
	proveit.numbers.ordering.relax_less
66	instantiation	75, 76	⊢
	:
67	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
68	instantiation	77, 78, 79	⊢
	:
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
70	instantiation	100, 80, 81	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.real_closure
72	instantiation	82, 83, 84, 85	⊢
	: , :
73	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
75	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
76	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
77	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
78	instantiation	100, 86, 87	⊢
	: , : , :
79	assumption		⊢
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
81	instantiation	100, 88, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.division.div_real_closure
83	instantiation	100, 90, 89	⊢
	: , : , :
84	instantiation	100, 90, 91	⊢
	: , : , :
85	instantiation	92, 93	⊢
	:
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
87	instantiation	94, 95	⊢
	:
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
89	instantiation	100, 97, 96	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
91	instantiation	100, 97, 98	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
93	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
94	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
95	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
96	instantiation	100, 101, 99	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
98	instantiation	100, 101, 102	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat2
*equality replacement requirements