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	77	⊢
2	instantiation	77, 4, 5	⊢
	: , : , :
3	instantiation	77, 6, 7	⊢
	: , : , :
4	instantiation	9, 17, 18, 115, 19, 12, 97, 32, 23, 8	⊢
	: , : , : , : , : , :
5	instantiation	9, 18, 122, 17, 12, 10, 19, 97, 32, 23, 22, 24	⊢
	: , : , : , : , : , :
6	instantiation	11, 17, 18, 115, 19, 12, 97, 32, 23, 22, 24	⊢
	: , : , : , : , : , : , :
7	instantiation	77, 13, 14	⊢
	: , : , :
8	instantiation	15, 22, 24	⊢
	: , :
9	theorem		⊢
	proveit.numbers.multiplication.disassociation
10	instantiation	26	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
12	instantiation	27	⊢
	: , : , :
13	instantiation	16, 17, 122, 18, 19, 20, 21, 22, 97, 32, 23, 24	⊢
	: , : , : , : , : , :
14	instantiation	86, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
16	theorem		⊢
	proveit.numbers.multiplication.association
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	26	⊢
	: , :
21	instantiation	27	⊢
	: , : , :
22	instantiation	28, 71, 97, 29	⊢
	: , :
23	instantiation	120, 103, 30	⊢
	: , : , :
24	instantiation	31, 32, 33	⊢
	: , :
25	instantiation	42, 34, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	theorem		⊢
	proveit.numbers.division.div_complex_closure
29	instantiation	36, 109	⊢
	:
30	instantiation	37, 38, 39	⊢
	: , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
32	instantiation	120, 103, 40	⊢
	: , : , :
33	instantiation	120, 103, 41	⊢
	: , : , :
34	instantiation	42, 43, 44	⊢
	: , : , :
35	instantiation	45, 46, 47, 48	⊢
	: , : , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
37	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
38	instantiation	49, 50	⊢
	:
39	instantiation	51, 52	⊢
	:
40	instantiation	120, 53, 54	⊢
	: , : , :
41	instantiation	120, 111, 55	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.sub_right_side_into
43	instantiation	56, 71, 57, 58	⊢
	: , : , : , : , :
44	instantiation	77, 59, 60	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
46	instantiation	86, 61	⊢
	: , : , :
47	instantiation	86, 61	⊢
	: , : , :
48	instantiation	96, 71	⊢
	:
49	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
50	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
51	theorem		⊢
	proveit.numbers.negation.real_closure
52	instantiation	62, 63, 64	⊢
	: , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
55	instantiation	120, 116, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
57	instantiation	120, 67, 66	⊢
	: , : , :
58	instantiation	120, 67, 68	⊢
	: , : , :
59	instantiation	86, 69	⊢
	: , : , :
60	instantiation	86, 70	⊢
	: , : , :
61	instantiation	88, 71	⊢
	:
62	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
63	instantiation	120, 111, 72	⊢
	: , : , :
64	instantiation	120, 111, 73	⊢
	: , : , :
65	instantiation	113, 107	⊢
	:
66	instantiation	120, 75, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
68	instantiation	120, 75, 93	⊢
	: , : , :
69	instantiation	86, 76	⊢
	: , : , :
70	instantiation	77, 78, 79	⊢
	: , : , :
71	instantiation	120, 103, 80	⊢
	: , : , :
72	instantiation	120, 116, 81	⊢
	: , : , :
73	instantiation	120, 82, 83	⊢
	: , : , :
74	instantiation	120, 100, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
76	instantiation	85, 97	⊢
	:
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	86, 87	⊢
	: , : , :
79	instantiation	88, 97	⊢
	:
80	instantiation	120, 111, 89	⊢
	: , : , :
81	instantiation	120, 90, 91	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
83	instantiation	92, 93, 94	⊢
	: , :
84	instantiation	120, 108, 95	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
86	axiom		⊢
	proveit.logic.equality.substitution
87	instantiation	96, 97	⊢
	:
88	theorem		⊢
	proveit.numbers.division.frac_one_denom
89	instantiation	120, 116, 107	⊢
	: , : , :
90	instantiation	98, 99, 114	⊢
	: , :
91	assumption		⊢
92	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
93	instantiation	120, 100, 101	⊢
	: , : , :
94	instantiation	113, 102	⊢
	:
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
96	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
97	instantiation	120, 103, 104	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
99	instantiation	105, 106, 107	⊢
	: , :
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
101	instantiation	120, 108, 109	⊢
	: , : , :
102	instantiation	120, 118, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
104	instantiation	120, 111, 112	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
106	instantiation	113, 114	⊢
	:
107	instantiation	120, 121, 115	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
110	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
112	instantiation	120, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.negation.int_closure
114	instantiation	120, 118, 119	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
117	instantiation	120, 121, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
119	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
120	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
121	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat2