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