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	30	⊢
2	instantiation	11, 4	,  ⊢
	: , : , :
3	instantiation	5, 37, 6	,  ⊢
	: , :
4	instantiation	43, 7, 8	,  ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.multiplication.commutation
6	instantiation	9, 19, 39, 10	⊢
	: , :
7	instantiation	11, 12	,  ⊢
	: , : , :
8	instantiation	13, 14	,  ⊢
	: , :
9	theorem		⊢
	proveit.numbers.division.div_complex_closure
10	instantiation	15, 96	⊢
	:
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	43, 16, 17	,  ⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	18, 37, 19, 20, 21, 22*, 23*	,  ⊢
	: , : , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
16	instantiation	24, 53, 25, 101, 54, 26, 65, 66, 57, 37, 58	,  ⊢
	: , : , : , : , : , : , :
17	instantiation	27, 101, 28, 53, 29, 54, 37, 65, 66, 57, 58	,  ⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.division.prod_of_fracs
19	instantiation	30, 31, 32	⊢
	: , : , :
20	instantiation	99, 34, 33	⊢
	: , : , :
21	instantiation	99, 34, 35	⊢
	: , : , :
22	instantiation	36, 37	⊢
	:
23	instantiation	38, 39	⊢
	:
24	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
26	instantiation	40	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.association
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
29	instantiation	41	⊢
	: , : , : , :
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	instantiation	64, 51, 42	⊢
	: , :
32	instantiation	43, 44, 45	⊢
	: , : , :
33	instantiation	99, 47, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35	instantiation	99, 47, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.division.frac_one_denom
37	instantiation	99, 73, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
39	instantiation	99, 73, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
42	instantiation	64, 57, 58	⊢
	: , :
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	52, 101, 86, 53, 56, 54, 51, 57, 58	⊢
	: , : , : , : , : , :
45	instantiation	52, 53, 86, 54, 55, 56, 65, 66, 57, 58	⊢
	: , : , : , : , : , :
46	instantiation	99, 60, 59	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
48	instantiation	99, 60, 61	⊢
	: , : , :
49	instantiation	99, 77, 62	⊢
	: , : , :
50	instantiation	99, 77, 63	⊢
	: , : , :
51	instantiation	64, 65, 66	⊢
	: , :
52	theorem		⊢
	proveit.numbers.multiplication.disassociation
53	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
54	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
55	instantiation	67	⊢
	: , :
56	instantiation	67	⊢
	: , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
58	instantiation	99, 73, 68	⊢
	: , : , :
59	instantiation	99, 70, 69	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	99, 70, 96	⊢
	: , : , :
62	instantiation	99, 82, 71	⊢
	: , : , :
63	instantiation	99, 82, 93	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
65	instantiation	99, 73, 72	⊢
	: , : , :
66	instantiation	99, 73, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	instantiation	99, 77, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
71	instantiation	99, 84, 76	⊢
	: , : , :
72	instantiation	99, 77, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	99, 79, 80	⊢
	: , : , :
75	instantiation	99, 82, 81	⊢
	: , : , :
76	assumption		⊢
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	99, 82, 83	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
81	instantiation	99, 84, 85	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	99, 100, 86	⊢
	: , : , :
84	instantiation	87, 88, 89	⊢
	: , :
85	instantiation	90, 91, 96	⊢
	: , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
87	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
88	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
89	instantiation	92, 93, 94	⊢
	: , :
90	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
91	assumption		⊢
92	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
93	instantiation	99, 95, 96	⊢
	: , : , :
94	instantiation	97, 98	⊢
	:
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
96	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
97	theorem		⊢
	proveit.numbers.negation.int_closure
98	instantiation	99, 100, 101	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements