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, 5, 6	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	133	⊢
3	instantiation	58	⊢
	: , :
4	instantiation	58	⊢
	: , :
5	instantiation	7, 12	⊢
	: , :
6	instantiation	8, 9	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
9	instantiation	10, 17, 11, 12	⊢
	: , :
10	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
11	instantiation	131, 120, 13	⊢
	: , : , :
12	instantiation	14, 15	⊢
	: , :
13	instantiation	131, 127, 34	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.relax_less
15	instantiation	16, 17, 18, 99, 19, 20*, 21*	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
17	instantiation	131, 120, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
20	instantiation	54, 23, 24, 25	⊢
	: , : , : , :
21	instantiation	54, 26, 27, 28	⊢
	: , : , : , :
22	instantiation	131, 127, 29	⊢
	: , : , :
23	instantiation	38, 30, 31	⊢
	: , : , :
24	instantiation	62	⊢
	:
25	instantiation	67, 37	⊢
	: , :
26	instantiation	38, 32, 33	⊢
	: , : , :
27	instantiation	62	⊢
	:
28	instantiation	67, 44	⊢
	: , :
29	instantiation	75, 34, 77	⊢
	: , :
30	instantiation	69, 37	⊢
	: , : , :
31	instantiation	38, 35, 36	⊢
	: , : , :
32	instantiation	69, 37	⊢
	: , : , :
33	instantiation	38, 39, 40	⊢
	: , : , :
34	instantiation	131, 92, 41	⊢
	: , : , :
35	instantiation	45, 126, 133, 46, 47, 48, 42, 50, 82	⊢
	: , : , : , : , : , :
36	instantiation	43, 46, 133, 48, 47, 50, 82	⊢
	: , : , : , :
37	instantiation	69, 44	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	45, 126, 133, 46, 47, 48, 87, 50, 82	⊢
	: , : , : , : , : , :
40	instantiation	49, 87, 50, 51	⊢
	: , : , :
41	instantiation	52, 133, 53	⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
43	theorem		⊢
	proveit.numbers.addition.elim_zero_any
44	instantiation	54, 55, 56, 57	⊢
	: , : , : , :
45	theorem		⊢
	proveit.numbers.addition.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	instantiation	58	⊢
	: , :
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
50	instantiation	59, 60, 61	⊢
	: , :
51	instantiation	62	⊢
	:
52	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
53	instantiation	63, 64, 65	⊢
	:
54	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
55	instantiation	69, 66	⊢
	: , : , :
56	instantiation	67, 68	⊢
	: , :
57	instantiation	69, 70	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
60	instantiation	71, 87, 72, 73	⊢
	: , :
61	instantiation	131, 111, 74	⊢
	: , : , :
62	axiom		⊢
	proveit.logic.equality.equals_reflexivity
63	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
64	instantiation	75, 76, 77	⊢
	: , :
65	instantiation	78, 79	⊢
	: , :
66	instantiation	80, 81, 82	⊢
	: , :
67	theorem		⊢
	proveit.logic.equality.equals_reversal
68	instantiation	83, 102, 96, 95, 89	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	84, 85, 130	⊢
	: , :
71	theorem		⊢
	proveit.numbers.division.div_complex_closure
72	instantiation	86, 102, 87	⊢
	: , :
73	instantiation	88, 89, 90	⊢
	: , : , :
74	instantiation	103, 104, 91	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
76	instantiation	131, 92, 105	⊢
	: , : , :
77	instantiation	131, 93, 123	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
79	instantiation	94, 105	⊢
	:
80	theorem		⊢
	proveit.numbers.addition.commutation
81	instantiation	131, 111, 95	⊢
	: , : , :
82	instantiation	131, 111, 96	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
84	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
85	instantiation	131, 97, 98	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
87	instantiation	131, 111, 99	⊢
	: , : , :
88	theorem		⊢
	proveit.logic.equality.sub_left_side_into
89	instantiation	100, 125	⊢
	:
90	instantiation	101, 102	⊢
	:
91	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
92	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
93	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
94	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
95	instantiation	103, 104, 105	⊢
	: , : , :
96	instantiation	131, 106, 107	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
98	instantiation	131, 108, 109	⊢
	: , : , :
99	instantiation	131, 120, 110	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
101	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
102	instantiation	131, 111, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
104	instantiation	113, 114	⊢
	: , :
105	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
107	instantiation	131, 115, 116	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
109	instantiation	131, 117, 118	⊢
	: , : , :
110	instantiation	131, 127, 119	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	instantiation	131, 120, 121	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
116	instantiation	131, 122, 123	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
118	instantiation	131, 124, 125	⊢
	: , : , :
119	instantiation	131, 132, 126	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
121	instantiation	131, 127, 128	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
123	instantiation	129, 130	⊢
	:
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
125	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
127	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
128	instantiation	131, 132, 133	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.negation.int_neg_closure
130	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements