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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
2	reference	9	⊢
3	instantiation	123, 112, 5	⊢
	: , : , :
4	instantiation	6, 7	⊢
	: , :
5	instantiation	123, 119, 26	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.ordering.relax_less
7	instantiation	8, 9, 10, 91, 11, 12*, 13*	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
9	instantiation	123, 112, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
11	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
12	instantiation	46, 15, 16, 17	⊢
	: , : , : , :
13	instantiation	46, 18, 19, 20	⊢
	: , : , : , :
14	instantiation	123, 119, 21	⊢
	: , : , :
15	instantiation	30, 22, 23	⊢
	: , : , :
16	instantiation	54	⊢
	:
17	instantiation	59, 29	⊢
	: , :
18	instantiation	30, 24, 25	⊢
	: , : , :
19	instantiation	54	⊢
	:
20	instantiation	59, 36	⊢
	: , :
21	instantiation	67, 26, 69	⊢
	: , :
22	instantiation	61, 29	⊢
	: , : , :
23	instantiation	30, 27, 28	⊢
	: , : , :
24	instantiation	61, 29	⊢
	: , : , :
25	instantiation	30, 31, 32	⊢
	: , : , :
26	instantiation	123, 84, 33	⊢
	: , : , :
27	instantiation	37, 118, 125, 38, 39, 40, 34, 42, 74	⊢
	: , : , : , : , : , :
28	instantiation	35, 38, 125, 40, 39, 42, 74	⊢
	: , : , : , :
29	instantiation	61, 36	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.equals_transitivity
31	instantiation	37, 118, 125, 38, 39, 40, 79, 42, 74	⊢
	: , : , : , : , : , :
32	instantiation	41, 79, 42, 43	⊢
	: , : , :
33	instantiation	44, 125, 45	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
35	theorem		⊢
	proveit.numbers.addition.elim_zero_any
36	instantiation	46, 47, 48, 49	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.addition.disassociation
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	instantiation	50	⊢
	: , :
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
42	instantiation	51, 52, 53	⊢
	: , :
43	instantiation	54	⊢
	:
44	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
45	instantiation	55, 56, 57	⊢
	:
46	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
47	instantiation	61, 58	⊢
	: , : , :
48	instantiation	59, 60	⊢
	: , :
49	instantiation	61, 62	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
51	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
52	instantiation	63, 79, 64, 65	⊢
	: , :
53	instantiation	123, 103, 66	⊢
	: , : , :
54	axiom		⊢
	proveit.logic.equality.equals_reflexivity
55	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
56	instantiation	67, 68, 69	⊢
	: , :
57	instantiation	70, 71	⊢
	: , :
58	instantiation	72, 73, 74	⊢
	: , :
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	75, 94, 88, 87, 81	⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	76, 77, 122	⊢
	: , :
63	theorem		⊢
	proveit.numbers.division.div_complex_closure
64	instantiation	78, 94, 79	⊢
	: , :
65	instantiation	80, 81, 82	⊢
	: , : , :
66	instantiation	95, 96, 83	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
68	instantiation	123, 84, 97	⊢
	: , : , :
69	instantiation	123, 85, 115	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
71	instantiation	86, 97	⊢
	:
72	theorem		⊢
	proveit.numbers.addition.commutation
73	instantiation	123, 103, 87	⊢
	: , : , :
74	instantiation	123, 103, 88	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
76	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
77	instantiation	123, 89, 90	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
79	instantiation	123, 103, 91	⊢
	: , : , :
80	theorem		⊢
	proveit.logic.equality.sub_left_side_into
81	instantiation	92, 117	⊢
	:
82	instantiation	93, 94	⊢
	:
83	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
85	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
86	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
87	instantiation	95, 96, 97	⊢
	: , : , :
88	instantiation	123, 98, 99	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	123, 100, 101	⊢
	: , : , :
91	instantiation	123, 112, 102	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
93	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
94	instantiation	123, 103, 104	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
96	instantiation	105, 106	⊢
	: , :
97	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
99	instantiation	123, 107, 108	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
101	instantiation	123, 109, 110	⊢
	: , : , :
102	instantiation	123, 119, 111	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
104	instantiation	123, 112, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
108	instantiation	123, 114, 115	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
110	instantiation	123, 116, 117	⊢
	: , : , :
111	instantiation	123, 124, 118	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
113	instantiation	123, 119, 120	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
115	instantiation	121, 122	⊢
	:
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
120	instantiation	123, 124, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.negation.int_neg_closure
122	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
123	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements