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