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