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.numbers.ordering.transitivity_less_less_eq
2	instantiation	4, 90, 91, 5	⊢
	: , : , :
3	instantiation	14, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
5	instantiation	8, 9, 10	⊢
	: , : , :
6	instantiation	11, 64	⊢
	:
7	instantiation	57, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	14, 41, 15	⊢
	: , : , :
10	instantiation	16, 17, 18	⊢
	: , :
11	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
12	instantiation	19, 20	⊢
	: , : , :
13	instantiation	21, 22, 23, 39, 24*, 25*	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_left_side_into
15	instantiation	26, 27	⊢
	:
16	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
17	instantiation	111, 85, 66	⊢
	: , : , :
18	instantiation	111, 85, 28	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.equality.substitution
20	instantiation	29, 30, 86, 91, 31, 32, 33*	⊢
	: , : , : , :
21	theorem		⊢
	proveit.numbers.division.frac_cancel_left
22	instantiation	111, 35, 34	⊢
	: , : , :
23	instantiation	111, 35, 36	⊢
	: , : , :
24	instantiation	37, 49	⊢
	:
25	instantiation	38, 39	⊢
	:
26	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
27	instantiation	40, 90, 91, 41	⊢
	: , : , :
28	instantiation	111, 97, 42	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
30	instantiation	111, 43, 44	⊢
	: , : , :
31	instantiation	45, 86, 84	⊢
	: , :
32	instantiation	46, 47	⊢
	: , :
33	instantiation	48, 49	⊢
	:
34	instantiation	111, 51, 50	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
36	instantiation	111, 51, 52	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	theorem		⊢
	proveit.numbers.division.frac_one_denom
39	instantiation	111, 85, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
41	instantiation	54, 66	⊢
	:
42	instantiation	111, 105, 55	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
44	instantiation	111, 56, 77	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
46	theorem		⊢
	proveit.logic.equality.equals_reversal
47	instantiation	57, 58, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
49	instantiation	111, 85, 60	⊢
	: , : , :
50	instantiation	111, 62, 61	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
52	instantiation	111, 62, 63	⊢
	: , : , :
53	instantiation	94, 95, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
55	instantiation	65, 66	⊢
	:
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
57	axiom		⊢
	proveit.logic.equality.equals_transitivity
58	instantiation	67, 113, 108, 68, 69, 70, 73, 74, 71	⊢
	: , : , : , : , : , :
59	instantiation	72, 73, 74, 75	⊢
	: , : , :
60	instantiation	111, 97, 76	⊢
	: , : , :
61	instantiation	111, 78, 77	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
63	instantiation	111, 78, 79	⊢
	: , : , :
64	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
65	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
66	instantiation	80, 81, 82	⊢
	: , :
67	theorem		⊢
	proveit.numbers.addition.disassociation
68	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
69	instantiation	83	⊢
	: , :
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	111, 85, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
73	instantiation	111, 85, 91	⊢
	: , : , :
74	instantiation	111, 85, 86	⊢
	: , : , :
75	instantiation	87	⊢
	:
76	instantiation	111, 105, 103	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
80	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
81	instantiation	111, 97, 88	⊢
	: , : , :
82	instantiation	89, 90, 91, 92	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
84	instantiation	111, 97, 93	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	94, 95, 110	⊢
	: , : , :
87	axiom		⊢
	proveit.logic.equality.equals_reflexivity
88	instantiation	111, 105, 96	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
91	instantiation	111, 97, 98	⊢
	: , : , :
92	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
93	instantiation	111, 105, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
95	instantiation	100, 101	⊢
	: , :
96	instantiation	102, 103, 104	⊢
	: , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	111, 105, 107	⊢
	: , : , :
99	instantiation	106, 107	⊢
	:
100	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
102	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
103	instantiation	111, 112, 108	⊢
	: , : , :
104	instantiation	111, 109, 110	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
106	theorem		⊢
	proveit.numbers.negation.int_closure
107	instantiation	111, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
109	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
110	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
111	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements