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