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*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
2	instantiation	62, 45, 6	⊢
	: , :
3	instantiation	7, 47, 103	⊢
	: , :
4	instantiation	8, 9	⊢
	: , :
5	instantiation	10, 11, 12*	⊢
	:
6	instantiation	13, 83	⊢
	:
7	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
8	theorem		⊢
	proveit.numbers.ordering.relax_less
9	instantiation	14, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
11	instantiation	17, 18	⊢
	: , :
12	instantiation	19, 35, 34	⊢
	: , :
13	theorem		⊢
	proveit.numbers.negation.real_closure
14	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
15	instantiation	20, 107, 108, 21	⊢
	: , : , :
16	instantiation	31, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.nonpos_difference
18	instantiation	24, 83	⊢
	:
19	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
21	instantiation	25, 26, 27	⊢
	: , : , :
22	instantiation	28, 81	⊢
	:
23	instantiation	74, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.rounding.floor_x_le_x
25	theorem		⊢
	proveit.logic.equality.sub_right_side_into
26	instantiation	31, 58, 32	⊢
	: , : , :
27	instantiation	33, 34, 35	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
29	instantiation	36, 37	⊢
	: , : , :
30	instantiation	38, 39, 40, 56, 41*, 42*	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.sub_left_side_into
32	instantiation	43, 44	⊢
	:
33	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
34	instantiation	128, 102, 83	⊢
	: , : , :
35	instantiation	128, 102, 45	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.substitution
37	instantiation	46, 47, 103, 108, 48, 49, 50*	⊢
	: , : , : , :
38	theorem		⊢
	proveit.numbers.division.frac_cancel_left
39	instantiation	128, 52, 51	⊢
	: , : , :
40	instantiation	128, 52, 53	⊢
	: , : , :
41	instantiation	54, 66	⊢
	:
42	instantiation	55, 56	⊢
	:
43	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
44	instantiation	57, 107, 108, 58	⊢
	: , : , :
45	instantiation	128, 114, 59	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
47	instantiation	128, 60, 61	⊢
	: , : , :
48	instantiation	62, 103, 101	⊢
	: , :
49	instantiation	63, 64	⊢
	: , :
50	instantiation	65, 66	⊢
	:
51	instantiation	128, 68, 67	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
53	instantiation	128, 68, 69	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
55	theorem		⊢
	proveit.numbers.division.frac_one_denom
56	instantiation	128, 102, 70	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
58	instantiation	71, 83	⊢
	:
59	instantiation	128, 122, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
61	instantiation	128, 73, 94	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
63	theorem		⊢
	proveit.logic.equality.equals_reversal
64	instantiation	74, 75, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
66	instantiation	128, 102, 77	⊢
	: , : , :
67	instantiation	128, 79, 78	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
69	instantiation	128, 79, 80	⊢
	: , : , :
70	instantiation	111, 112, 81	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
72	instantiation	82, 83	⊢
	:
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
74	axiom		⊢
	proveit.logic.equality.equals_transitivity
75	instantiation	84, 130, 125, 85, 86, 87, 90, 91, 88	⊢
	: , : , : , : , : , :
76	instantiation	89, 90, 91, 92	⊢
	: , : , :
77	instantiation	128, 114, 93	⊢
	: , : , :
78	instantiation	128, 95, 94	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80	instantiation	128, 95, 96	⊢
	: , : , :
81	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
82	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
83	instantiation	97, 98, 99	⊢
	: , :
84	theorem		⊢
	proveit.numbers.addition.disassociation
85	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
86	instantiation	100	⊢
	: , :
87	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
88	instantiation	128, 102, 101	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
90	instantiation	128, 102, 108	⊢
	: , : , :
91	instantiation	128, 102, 103	⊢
	: , : , :
92	instantiation	104	⊢
	:
93	instantiation	128, 122, 120	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
98	instantiation	128, 114, 105	⊢
	: , : , :
99	instantiation	106, 107, 108, 109	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	instantiation	128, 114, 110	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
103	instantiation	111, 112, 127	⊢
	: , : , :
104	axiom		⊢
	proveit.logic.equality.equals_reflexivity
105	instantiation	128, 122, 113	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
108	instantiation	128, 114, 115	⊢
	: , : , :
109	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
110	instantiation	128, 122, 116	⊢
	: , : , :
111	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
112	instantiation	117, 118	⊢
	: , :
113	instantiation	119, 120, 121	⊢
	: , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
115	instantiation	128, 122, 124	⊢
	: , : , :
116	instantiation	123, 124	⊢
	:
117	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
119	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
120	instantiation	128, 129, 125	⊢
	: , : , :
121	instantiation	128, 126, 127	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
123	theorem		⊢
	proveit.numbers.negation.int_closure
124	instantiation	128, 129, 130	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
126	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
127	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements