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.absolute_value.abs_neg_elim
2	instantiation	4, 15, 53, 22, 5, 6*, 7*	⊢
	: , : , :
3	instantiation	8, 10, 43, 9*	⊢
	: , :
4	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
5	instantiation	93, 47	⊢
	:
6	instantiation	57, 43, 10	⊢
	: , :
7	instantiation	16, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
9	instantiation	13, 14	⊢
	:
10	instantiation	107, 71, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , : , :
12	instantiation	19, 20, 21	⊢
	: , :
13	theorem		⊢
	proveit.numbers.negation.double_negation
14	instantiation	107, 71, 22	⊢
	: , : , :
15	instantiation	107, 86, 23	⊢
	: , : , :
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	51, 31	⊢
	: , : , :
18	instantiation	51, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
20	instantiation	25, 26, 27	⊢
	: , :
21	instantiation	28	⊢
	:
22	instantiation	107, 86, 29	⊢
	: , : , :
23	instantiation	107, 99, 30	⊢
	: , : , :
24	instantiation	51, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
26	instantiation	32, 43, 33, 34	⊢
	: , :
27	instantiation	107, 71, 35	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_reflexivity
29	instantiation	107, 99, 37	⊢
	: , : , :
30	instantiation	36, 37	⊢
	:
31	instantiation	38, 39, 40, 41	⊢
	: , : , : , :
32	theorem		⊢
	proveit.numbers.division.div_complex_closure
33	instantiation	42, 61, 43	⊢
	: , :
34	instantiation	44, 62, 45	⊢
	: , : , :
35	instantiation	82, 83, 46	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.int_closure
37	instantiation	107, 91, 47	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
39	instantiation	51, 48	⊢
	: , : , :
40	instantiation	49, 50	⊢
	: , :
41	instantiation	51, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
43	instantiation	107, 71, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.equality.sub_left_side_into
45	instantiation	54, 61	⊢
	:
46	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47	instantiation	55, 106, 56	⊢
	: , :
48	instantiation	57, 58, 59	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.equals_reversal
50	instantiation	60, 61, 70, 69, 62	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.substitution
52	instantiation	63, 64, 111	⊢
	: , :
53	instantiation	107, 86, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
55	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
56	instantiation	66, 67, 68	⊢
	:
57	theorem		⊢
	proveit.numbers.addition.commutation
58	instantiation	107, 71, 69	⊢
	: , : , :
59	instantiation	107, 71, 70	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
61	instantiation	107, 71, 72	⊢
	: , : , :
62	instantiation	73, 109	⊢
	:
63	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
64	instantiation	107, 74, 75	⊢
	: , : , :
65	instantiation	107, 99, 76	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
67	instantiation	77, 78, 79	⊢
	: , :
68	instantiation	80, 81	⊢
	: , :
69	instantiation	82, 83, 94	⊢
	: , : , :
70	instantiation	107, 84, 85	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	107, 86, 87	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
75	instantiation	107, 88, 89	⊢
	: , : , :
76	instantiation	107, 105, 90	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
78	instantiation	107, 91, 94	⊢
	: , : , :
79	instantiation	107, 92, 104	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
81	instantiation	93, 94	⊢
	:
82	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
83	instantiation	95, 96	⊢
	: , :
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
85	instantiation	107, 97, 98	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
87	instantiation	107, 99, 100	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
89	instantiation	107, 101, 102	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
92	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
93	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
94	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
95	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
98	instantiation	107, 103, 104	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
100	instantiation	107, 105, 106	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
102	instantiation	107, 108, 109	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
104	instantiation	110, 111	⊢
	:
105	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
110	theorem		⊢
	proveit.numbers.negation.int_neg_closure
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements