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	,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.ordering.relax_less
2	instantiation	3, 4, 5	,  ⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
4	instantiation	6, 21, 95, 7, 8, 9*, 10*	⊢
	: , : , :
5	instantiation	46, 11, 12	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	91, 92, 81	⊢
	: , : , :
8	instantiation	13, 81	⊢
	:
9	instantiation	70, 85, 14	⊢
	: , :
10	instantiation	22, 15, 16	⊢
	: , : , :
11	instantiation	17, 18	⊢
	:
12	instantiation	58, 19, 68, 20	,  ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
14	instantiation	111, 94, 21	⊢
	: , : , :
15	instantiation	22, 23, 24	⊢
	: , : , :
16	instantiation	25, 26, 27	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
18	instantiation	28, 29, 79	⊢
	: , :
19	instantiation	67, 37, 107	⊢
	: , :
20	assumption		⊢
21	instantiation	111, 101, 30	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	64, 40	⊢
	: , : , :
24	instantiation	64, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
26	instantiation	32, 33, 34	⊢
	: , :
27	instantiation	35	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
29	instantiation	36, 37, 38	⊢
	:
30	instantiation	111, 106, 39	⊢
	: , : , :
31	instantiation	64, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
33	instantiation	41, 85, 42, 43	⊢
	: , :
34	instantiation	111, 94, 44	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_reflexivity
36	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
37	instantiation	111, 45, 60	⊢
	: , : , :
38	instantiation	46, 47, 48	⊢
	: , : , :
39	instantiation	82, 68	⊢
	:
40	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
41	theorem		⊢
	proveit.numbers.division.div_complex_closure
42	instantiation	53, 74, 85	⊢
	: , :
43	instantiation	54, 76, 55	⊢
	: , : , :
44	instantiation	91, 92, 56	⊢
	: , : , :
45	instantiation	57, 107, 59	⊢
	: , :
46	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
47	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
48	instantiation	58, 107, 59, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	64, 61	⊢
	: , : , :
51	instantiation	62, 63	⊢
	: , :
52	instantiation	64, 65	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
54	theorem		⊢
	proveit.logic.equality.sub_left_side_into
55	instantiation	66, 74	⊢
	:
56	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
57	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
58	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
59	instantiation	67, 68, 69	⊢
	: , :
60	assumption		⊢
61	instantiation	70, 71, 72	⊢
	: , :
62	theorem		⊢
	proveit.logic.equality.equals_reversal
63	instantiation	73, 74, 75, 83, 76	⊢
	: , : , :
64	axiom		⊢
	proveit.logic.equality.substitution
65	instantiation	77, 78, 79	⊢
	: , :
66	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
67	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
68	instantiation	111, 80, 81	⊢
	: , : , :
69	instantiation	82, 103	⊢
	:
70	theorem		⊢
	proveit.numbers.addition.commutation
71	instantiation	111, 94, 83	⊢
	: , : , :
72	instantiation	84, 85	⊢
	:
73	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
74	instantiation	111, 94, 86	⊢
	: , : , :
75	instantiation	87, 95	⊢
	:
76	instantiation	88, 110	⊢
	:
77	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
78	instantiation	111, 89, 90	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
81	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
82	theorem		⊢
	proveit.numbers.negation.int_closure
83	instantiation	91, 92, 93	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.negation.complex_closure
85	instantiation	111, 94, 95	⊢
	: , : , :
86	instantiation	111, 101, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.negation.real_closure
88	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	111, 97, 98	⊢
	: , : , :
91	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
92	instantiation	99, 100	⊢
	: , :
93	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
95	instantiation	111, 101, 102	⊢
	: , : , :
96	instantiation	111, 106, 103	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
98	instantiation	111, 104, 105	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
102	instantiation	111, 106, 107	⊢
	: , : , :
103	instantiation	111, 112, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
105	instantiation	111, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
107	instantiation	111, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
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