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.ordering.transitivity_less_eq_less
2	instantiation	4, 19, 93, 5, 6, 7*, 8*	⊢
	: , : , :
3	instantiation	44, 9, 10	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
5	instantiation	89, 90, 79	⊢
	: , : , :
6	instantiation	11, 79	⊢
	:
7	instantiation	68, 83, 12	⊢
	: , :
8	instantiation	20, 13, 14	⊢
	: , : , :
9	instantiation	15, 16	⊢
	:
10	instantiation	56, 17, 66, 18	,  ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
12	instantiation	109, 92, 19	⊢
	: , : , :
13	instantiation	20, 21, 22	⊢
	: , : , :
14	instantiation	23, 24, 25	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16	instantiation	26, 27, 77	⊢
	: , :
17	instantiation	65, 35, 105	⊢
	: , :
18	assumption		⊢
19	instantiation	109, 99, 28	⊢
	: , : , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	62, 38	⊢
	: , : , :
22	instantiation	62, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
24	instantiation	30, 31, 32	⊢
	: , :
25	instantiation	33	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
27	instantiation	34, 35, 36	⊢
	:
28	instantiation	109, 104, 37	⊢
	: , : , :
29	instantiation	62, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
31	instantiation	39, 83, 40, 41	⊢
	: , :
32	instantiation	109, 92, 42	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_reflexivity
34	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
35	instantiation	109, 43, 58	⊢
	: , : , :
36	instantiation	44, 45, 46	⊢
	: , : , :
37	instantiation	80, 66	⊢
	:
38	instantiation	47, 48, 49, 50	⊢
	: , : , : , :
39	theorem		⊢
	proveit.numbers.division.div_complex_closure
40	instantiation	51, 72, 83	⊢
	: , :
41	instantiation	52, 74, 53	⊢
	: , : , :
42	instantiation	89, 90, 54	⊢
	: , : , :
43	instantiation	55, 105, 57	⊢
	: , :
44	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
45	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
46	instantiation	56, 105, 57, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
48	instantiation	62, 59	⊢
	: , : , :
49	instantiation	60, 61	⊢
	: , :
50	instantiation	62, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
52	theorem		⊢
	proveit.logic.equality.sub_left_side_into
53	instantiation	64, 72	⊢
	:
54	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
57	instantiation	65, 66, 67	⊢
	: , :
58	assumption		⊢
59	instantiation	68, 69, 70	⊢
	: , :
60	theorem		⊢
	proveit.logic.equality.equals_reversal
61	instantiation	71, 72, 73, 81, 74	⊢
	: , : , :
62	axiom		⊢
	proveit.logic.equality.substitution
63	instantiation	75, 76, 77	⊢
	: , :
64	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
65	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
66	instantiation	109, 78, 79	⊢
	: , : , :
67	instantiation	80, 101	⊢
	:
68	theorem		⊢
	proveit.numbers.addition.commutation
69	instantiation	109, 92, 81	⊢
	: , : , :
70	instantiation	82, 83	⊢
	:
71	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
72	instantiation	109, 92, 84	⊢
	: , : , :
73	instantiation	85, 93	⊢
	:
74	instantiation	86, 108	⊢
	:
75	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
76	instantiation	109, 87, 88	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
79	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
80	theorem		⊢
	proveit.numbers.negation.int_closure
81	instantiation	89, 90, 91	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.negation.complex_closure
83	instantiation	109, 92, 93	⊢
	: , : , :
84	instantiation	109, 99, 94	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.negation.real_closure
86	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
88	instantiation	109, 95, 96	⊢
	: , : , :
89	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
90	instantiation	97, 98	⊢
	: , :
91	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
93	instantiation	109, 99, 100	⊢
	: , : , :
94	instantiation	109, 104, 101	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
96	instantiation	109, 102, 103	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
100	instantiation	109, 104, 105	⊢
	: , : , :
101	instantiation	109, 110, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
103	instantiation	109, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
105	instantiation	109, 110, 111	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
107	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
108	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
109	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements