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	⊢
	: , : , :
1	reference	21	⊢
2	instantiation	3, 4, 5, 6, 7, 8	⊢
	: , : , :
3	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
5	instantiation	81	⊢
	: , :
6	instantiation	81	⊢
	: , :
7	instantiation	21, 9	⊢
	: , : , :
8	instantiation	10	⊢
	:
9	instantiation	21, 11	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.equals_reflexivity
11	instantiation	47, 12, 13	⊢
	: , : , :
12	instantiation	21, 14	⊢
	: , : , :
13	instantiation	47, 15, 16	⊢
	: , : , :
14	instantiation	68, 37, 95, 69, 38, 17, 70, 73, 74, 79, 80, 42, 72	⊢
	: , : , : , : , : , :
15	instantiation	47, 18, 19	⊢
	: , : , :
16	instantiation	20, 26	⊢
	:
17	instantiation	81	⊢
	: , :
18	instantiation	21, 22	⊢
	: , : , :
19	instantiation	23, 24, 25, 26, 27*	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.division.frac_one_denom
21	axiom		⊢
	proveit.logic.equality.substitution
22	instantiation	47, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.division.frac_cancel_left
24	instantiation	108, 31, 30	⊢
	: , : , :
25	instantiation	108, 31, 32	⊢
	: , : , :
26	instantiation	56, 33, 34	⊢
	: , : , :
27	instantiation	35, 42	⊢
	:
28	instantiation	36, 69, 37, 110, 70, 38, 73, 74, 79, 80, 42, 72	⊢
	: , : , : , : , : , : , :
29	instantiation	39, 110, 40, 69, 41, 70, 42, 73, 74, 79, 80, 72	⊢
	: , : , : , : , : , :
30	instantiation	108, 44, 43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32	instantiation	108, 44, 45	⊢
	: , : , :
33	instantiation	78, 59, 46	⊢
	: , :
34	instantiation	47, 48, 49	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
36	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
38	instantiation	50	⊢
	: , : , : , :
39	theorem		⊢
	proveit.numbers.multiplication.association
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
41	instantiation	51	⊢
	: , : , : , : , :
42	instantiation	108, 85, 52	⊢
	: , : , :
43	instantiation	108, 54, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
45	instantiation	108, 54, 55	⊢
	: , : , :
46	instantiation	56, 57, 58	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_transitivity
48	instantiation	68, 110, 60, 69, 62, 70, 59, 79, 80, 72	⊢
	: , : , : , : , : , :
49	instantiation	68, 69, 95, 60, 70, 61, 62, 73, 74, 79, 80, 72	⊢
	: , : , : , : , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
52	instantiation	63, 64, 105	⊢
	: , : , :
53	instantiation	108, 65, 105	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
55	instantiation	108, 65, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.equality.sub_right_side_into
57	instantiation	78, 67, 72	⊢
	: , :
58	instantiation	68, 69, 95, 110, 70, 71, 79, 80, 72	⊢
	: , : , : , : , : , :
59	instantiation	78, 73, 74	⊢
	: , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	instantiation	81	⊢
	: , :
62	instantiation	75	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
64	instantiation	76, 77	⊢
	: , :
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	instantiation	78, 79, 80	⊢
	: , :
68	theorem		⊢
	proveit.numbers.multiplication.disassociation
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	81	⊢
	: , :
72	instantiation	108, 85, 82	⊢
	: , : , :
73	instantiation	108, 85, 83	⊢
	: , : , :
74	instantiation	108, 85, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
76	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
80	instantiation	108, 85, 86	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
82	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
83	instantiation	108, 90, 87	⊢
	: , : , :
84	instantiation	108, 88, 89	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	108, 90, 91	⊢
	: , : , :
87	instantiation	108, 93, 92	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
91	instantiation	108, 93, 94	⊢
	: , : , :
92	instantiation	108, 109, 95	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
94	instantiation	108, 96, 97	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
96	instantiation	98, 99, 100	⊢
	: , :
97	assumption		⊢
98	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
99	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
100	instantiation	101, 102, 103	⊢
	: , :
101	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
102	instantiation	108, 104, 105	⊢
	: , : , :
103	instantiation	106, 107	⊢
	:
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
105	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
106	theorem		⊢
	proveit.numbers.negation.int_closure
107	instantiation	108, 109, 110	⊢
	: , : , :
108	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements