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*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
2	reference	12	⊢
3	reference	48	⊢
4	instantiation	71, 72, 42	⊢
	: , : , :
5	instantiation	8, 42	⊢
	:
6	instantiation	51, 37, 9	⊢
	: , :
7	instantiation	13, 10, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
9	instantiation	91, 65, 12	⊢
	: , : , :
10	instantiation	13, 14, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , :
12	instantiation	91, 75, 19	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	46, 26	⊢
	: , : , :
15	instantiation	46, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
17	instantiation	21, 22, 23	⊢
	: , :
18	instantiation	24	⊢
	:
19	instantiation	91, 82, 25	⊢
	: , : , :
20	instantiation	46, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
22	instantiation	27, 37, 28, 29	⊢
	: , :
23	instantiation	91, 65, 30	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	instantiation	86, 31	⊢
	:
26	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.division.div_complex_closure
28	instantiation	36, 55, 37	⊢
	: , :
29	instantiation	38, 56, 39	⊢
	: , : , :
30	instantiation	91, 75, 40	⊢
	: , : , :
31	instantiation	91, 41, 42	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	46, 43	⊢
	: , : , :
34	instantiation	44, 45	⊢
	: , :
35	instantiation	46, 47	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
37	instantiation	91, 65, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.sub_left_side_into
39	instantiation	49, 55	⊢
	:
40	instantiation	91, 82, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
43	instantiation	51, 52, 53	⊢
	: , :
44	theorem		⊢
	proveit.logic.equality.equals_reversal
45	instantiation	54, 55, 64, 63, 56	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	57, 58, 59	⊢
	: , :
48	instantiation	91, 75, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
50	instantiation	61, 83, 62	⊢
	: , :
51	theorem		⊢
	proveit.numbers.addition.commutation
52	instantiation	91, 65, 63	⊢
	: , : , :
53	instantiation	91, 65, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
55	instantiation	91, 65, 66	⊢
	: , : , :
56	instantiation	67, 90	⊢
	:
57	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
58	instantiation	91, 68, 69	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
60	instantiation	91, 82, 87	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
62	instantiation	91, 70, 73	⊢
	: , : , :
63	instantiation	71, 72, 73	⊢
	: , : , :
64	instantiation	91, 75, 74	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	instantiation	91, 75, 76	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69	instantiation	91, 77, 78	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
71	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
72	instantiation	79, 80	⊢
	: , :
73	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
74	instantiation	91, 82, 81	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	91, 82, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	91, 84, 85	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
81	instantiation	86, 87	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	91, 92, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
85	instantiation	91, 89, 90	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.negation.int_closure
87	instantiation	91, 92, 93	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
91	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
92	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements