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