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