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