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