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	reference	46	⊢
2	instantiation	4, 25, 19	⊢
	: , :
3	instantiation	5, 19, 25, 6*	⊢
	: , :
4	theorem		⊢
	proveit.numbers.ordering.max_bin_args_commute
5	axiom		⊢
	proveit.numbers.ordering.max_def_bin
6	instantiation	46, 7, 8	⊢
	: , : , :
7	instantiation	9, 141, 10, 11, 12, 13	⊢
	: , : , : , :
8	instantiation	14, 54, 134, 56	⊢
	: , : , : , : , :
9	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
10	instantiation	66	⊢
	: , :
11	instantiation	66	⊢
	: , :
12	instantiation	15, 20	⊢
	: , :
13	instantiation	16, 17	⊢
	: , :
14	axiom		⊢
	proveit.core_expr_types.conditionals.true_case_reduction
15	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
16	theorem		⊢
	proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
17	instantiation	18, 25, 19, 20	⊢
	: , :
18	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
19	instantiation	139, 128, 21	⊢
	: , : , :
20	instantiation	22, 23	⊢
	: , :
21	instantiation	139, 135, 42	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.ordering.relax_less
23	instantiation	24, 25, 26, 107, 27, 28*, 29*	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
25	instantiation	139, 128, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
28	instantiation	62, 31, 32, 33	⊢
	: , : , : , :
29	instantiation	62, 34, 35, 36	⊢
	: , : , : , :
30	instantiation	139, 135, 37	⊢
	: , : , :
31	instantiation	46, 38, 39	⊢
	: , : , :
32	instantiation	70	⊢
	:
33	instantiation	75, 45	⊢
	: , :
34	instantiation	46, 40, 41	⊢
	: , : , :
35	instantiation	70	⊢
	:
36	instantiation	75, 52	⊢
	: , :
37	instantiation	83, 42, 85	⊢
	: , :
38	instantiation	77, 45	⊢
	: , : , :
39	instantiation	46, 43, 44	⊢
	: , : , :
40	instantiation	77, 45	⊢
	: , : , :
41	instantiation	46, 47, 48	⊢
	: , : , :
42	instantiation	139, 100, 49	⊢
	: , : , :
43	instantiation	53, 134, 141, 54, 55, 56, 50, 58, 90	⊢
	: , : , : , : , : , :
44	instantiation	51, 54, 141, 56, 55, 58, 90	⊢
	: , : , : , :
45	instantiation	77, 52	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	53, 134, 141, 54, 55, 56, 95, 58, 90	⊢
	: , : , : , : , : , :
48	instantiation	57, 95, 58, 59	⊢
	: , : , :
49	instantiation	60, 141, 61	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
51	theorem		⊢
	proveit.numbers.addition.elim_zero_any
52	instantiation	62, 63, 64, 65	⊢
	: , : , : , :
53	theorem		⊢
	proveit.numbers.addition.disassociation
54	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
55	instantiation	66	⊢
	: , :
56	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
57	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
58	instantiation	67, 68, 69	⊢
	: , :
59	instantiation	70	⊢
	:
60	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
61	instantiation	71, 72, 73	⊢
	:
62	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
63	instantiation	77, 74	⊢
	: , : , :
64	instantiation	75, 76	⊢
	: , :
65	instantiation	77, 78	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
68	instantiation	79, 95, 80, 81	⊢
	: , :
69	instantiation	139, 119, 82	⊢
	: , : , :
70	axiom		⊢
	proveit.logic.equality.equals_reflexivity
71	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
72	instantiation	83, 84, 85	⊢
	: , :
73	instantiation	86, 87	⊢
	: , :
74	instantiation	88, 89, 90	⊢
	: , :
75	theorem		⊢
	proveit.logic.equality.equals_reversal
76	instantiation	91, 110, 104, 103, 97	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.substitution
78	instantiation	92, 93, 138	⊢
	: , :
79	theorem		⊢
	proveit.numbers.division.div_complex_closure
80	instantiation	94, 110, 95	⊢
	: , :
81	instantiation	96, 97, 98	⊢
	: , : , :
82	instantiation	111, 112, 99	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
84	instantiation	139, 100, 113	⊢
	: , : , :
85	instantiation	139, 101, 131	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
87	instantiation	102, 113	⊢
	:
88	theorem		⊢
	proveit.numbers.addition.commutation
89	instantiation	139, 119, 103	⊢
	: , : , :
90	instantiation	139, 119, 104	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
92	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
93	instantiation	139, 105, 106	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
95	instantiation	139, 119, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.logic.equality.sub_left_side_into
97	instantiation	108, 133	⊢
	:
98	instantiation	109, 110	⊢
	:
99	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
101	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
102	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
103	instantiation	111, 112, 113	⊢
	: , : , :
104	instantiation	139, 114, 115	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
106	instantiation	139, 116, 117	⊢
	: , : , :
107	instantiation	139, 128, 118	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
109	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
110	instantiation	139, 119, 120	⊢
	: , : , :
111	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
112	instantiation	121, 122	⊢
	: , :
113	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
115	instantiation	139, 123, 124	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
117	instantiation	139, 125, 126	⊢
	: , : , :
118	instantiation	139, 135, 127	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
120	instantiation	139, 128, 129	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
124	instantiation	139, 130, 131	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
126	instantiation	139, 132, 133	⊢
	: , : , :
127	instantiation	139, 140, 134	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
129	instantiation	139, 135, 136	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
131	instantiation	137, 138	⊢
	:
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
136	instantiation	139, 140, 141	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.negation.int_neg_closure
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
139	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements