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.core_expr_types.conditionals.dissatisfied_condition_reduction
2	instantiation	3, 10, 4, 5	⊢
	: , :
3	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
4	instantiation	124, 113, 6	⊢
	: , : , :
5	instantiation	7, 8	⊢
	: , :
6	instantiation	124, 120, 27	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.ordering.relax_less
8	instantiation	9, 10, 11, 92, 12, 13*, 14*	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
10	instantiation	124, 113, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
13	instantiation	47, 16, 17, 18	⊢
	: , : , : , :
14	instantiation	47, 19, 20, 21	⊢
	: , : , : , :
15	instantiation	124, 120, 22	⊢
	: , : , :
16	instantiation	31, 23, 24	⊢
	: , : , :
17	instantiation	55	⊢
	:
18	instantiation	60, 30	⊢
	: , :
19	instantiation	31, 25, 26	⊢
	: , : , :
20	instantiation	55	⊢
	:
21	instantiation	60, 37	⊢
	: , :
22	instantiation	68, 27, 70	⊢
	: , :
23	instantiation	62, 30	⊢
	: , : , :
24	instantiation	31, 28, 29	⊢
	: , : , :
25	instantiation	62, 30	⊢
	: , : , :
26	instantiation	31, 32, 33	⊢
	: , : , :
27	instantiation	124, 85, 34	⊢
	: , : , :
28	instantiation	38, 119, 126, 39, 40, 41, 35, 43, 75	⊢
	: , : , : , : , : , :
29	instantiation	36, 39, 126, 41, 40, 43, 75	⊢
	: , : , : , :
30	instantiation	62, 37	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	38, 119, 126, 39, 40, 41, 80, 43, 75	⊢
	: , : , : , : , : , :
33	instantiation	42, 80, 43, 44	⊢
	: , : , :
34	instantiation	45, 126, 46	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
36	theorem		⊢
	proveit.numbers.addition.elim_zero_any
37	instantiation	47, 48, 49, 50	⊢
	: , : , : , :
38	theorem		⊢
	proveit.numbers.addition.disassociation
39	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
40	instantiation	51	⊢
	: , :
41	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
43	instantiation	52, 53, 54	⊢
	: , :
44	instantiation	55	⊢
	:
45	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
46	instantiation	56, 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.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
53	instantiation	64, 80, 65, 66	⊢
	: , :
54	instantiation	124, 104, 67	⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.equals_reflexivity
56	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
57	instantiation	68, 69, 70	⊢
	: , :
58	instantiation	71, 72	⊢
	: , :
59	instantiation	73, 74, 75	⊢
	: , :
60	theorem		⊢
	proveit.logic.equality.equals_reversal
61	instantiation	76, 95, 89, 88, 82	⊢
	: , : , :
62	axiom		⊢
	proveit.logic.equality.substitution
63	instantiation	77, 78, 123	⊢
	: , :
64	theorem		⊢
	proveit.numbers.division.div_complex_closure
65	instantiation	79, 95, 80	⊢
	: , :
66	instantiation	81, 82, 83	⊢
	: , : , :
67	instantiation	96, 97, 84	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
69	instantiation	124, 85, 98	⊢
	: , : , :
70	instantiation	124, 86, 116	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
72	instantiation	87, 98	⊢
	:
73	theorem		⊢
	proveit.numbers.addition.commutation
74	instantiation	124, 104, 88	⊢
	: , : , :
75	instantiation	124, 104, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
77	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
78	instantiation	124, 90, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
80	instantiation	124, 104, 92	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.equality.sub_left_side_into
82	instantiation	93, 118	⊢
	:
83	instantiation	94, 95	⊢
	:
84	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
86	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
87	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
88	instantiation	96, 97, 98	⊢
	: , : , :
89	instantiation	124, 99, 100	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
91	instantiation	124, 101, 102	⊢
	: , : , :
92	instantiation	124, 113, 103	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
94	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
95	instantiation	124, 104, 105	⊢
	: , : , :
96	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
97	instantiation	106, 107	⊢
	: , :
98	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
100	instantiation	124, 108, 109	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
102	instantiation	124, 110, 111	⊢
	: , : , :
103	instantiation	124, 120, 112	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
105	instantiation	124, 113, 114	⊢
	: , : , :
106	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
109	instantiation	124, 115, 116	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
111	instantiation	124, 117, 118	⊢
	: , : , :
112	instantiation	124, 125, 119	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	124, 120, 121	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
116	instantiation	122, 123	⊢
	:
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
118	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	124, 125, 126	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.negation.int_neg_closure
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
124	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements