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_eq
2	instantiation	4, 17, 63, 5, 6, 7*, 8*	⊢
	: , : , :
3	instantiation	9, 10	⊢
	: , :
4	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
5	instantiation	91, 92, 82	⊢
	: , : , :
6	instantiation	11, 82	⊢
	:
7	instantiation	69, 50, 12	⊢
	: , :
8	instantiation	18, 13, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.ordering.relax_less
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
12	instantiation	111, 85, 17	⊢
	: , : , :
13	instantiation	18, 19, 20	⊢
	: , : , :
14	instantiation	21, 22, 23	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16	instantiation	24, 25, 77	⊢
	: , :
17	instantiation	111, 95, 26	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	61, 36	⊢
	: , : , :
20	instantiation	61, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
22	instantiation	28, 29, 30	⊢
	: , :
23	instantiation	31	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
25	instantiation	32, 33, 34	⊢
	:
26	instantiation	111, 102, 35	⊢
	: , : , :
27	instantiation	61, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
29	instantiation	37, 50, 38, 39	⊢
	: , :
30	instantiation	111, 85, 40	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_reflexivity
32	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
33	instantiation	111, 41, 57	⊢
	: , : , :
34	instantiation	42, 43, 44	⊢
	: , : , :
35	instantiation	106, 67	⊢
	:
36	instantiation	45, 46, 47, 48	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.division.div_complex_closure
38	instantiation	49, 73, 50	⊢
	: , :
39	instantiation	51, 74, 52	⊢
	: , : , :
40	instantiation	111, 95, 53	⊢
	: , : , :
41	instantiation	54, 107, 56	⊢
	: , :
42	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
43	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
44	instantiation	55, 107, 56, 57	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
46	instantiation	61, 58	⊢
	: , : , :
47	instantiation	59, 60	⊢
	: , :
48	instantiation	61, 62	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
50	instantiation	111, 85, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.equality.sub_left_side_into
52	instantiation	64, 73	⊢
	:
53	instantiation	111, 102, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
55	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
56	instantiation	66, 67, 68	⊢
	: , :
57	assumption		⊢
58	instantiation	69, 70, 71	⊢
	: , :
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	72, 73, 84, 83, 74	⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	75, 76, 77	⊢
	: , :
63	instantiation	111, 95, 78	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
65	instantiation	79, 103, 80	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	111, 81, 82	⊢
	: , : , :
68	instantiation	106, 103	⊢
	:
69	theorem		⊢
	proveit.numbers.addition.commutation
70	instantiation	111, 85, 83	⊢
	: , : , :
71	instantiation	111, 85, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
73	instantiation	111, 85, 86	⊢
	: , : , :
74	instantiation	87, 110	⊢
	:
75	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
76	instantiation	111, 88, 89	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
78	instantiation	111, 102, 107	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
80	instantiation	111, 90, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
82	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
83	instantiation	91, 92, 93	⊢
	: , : , :
84	instantiation	111, 95, 94	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	111, 95, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
89	instantiation	111, 97, 98	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
91	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
92	instantiation	99, 100	⊢
	: , :
93	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
94	instantiation	111, 102, 101	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
96	instantiation	111, 102, 103	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
98	instantiation	111, 104, 105	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
101	instantiation	106, 107	⊢
	:
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
103	instantiation	111, 112, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
105	instantiation	111, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.int_closure
107	instantiation	111, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
111	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements