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	reference	43	⊢
2	instantiation	5, 6, 7, 8, 27, 9, 10, 11, 12*	⊢
	: , : , : , :
3	instantiation	70, 13	⊢
	: , :
4	instantiation	70, 14	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
7	instantiation	36	⊢
	: , : , : , : , :
8	instantiation	36	⊢
	: , : , : , : , :
9	instantiation	16, 23, 28	⊢
	: , : , :
10	instantiation	16, 15, 29	⊢
	: , : , :
11	instantiation	16, 17, 30	⊢
	: , : , :
12	instantiation	92, 18, 19	⊢
	: , : , :
13	instantiation	75, 114, 80, 79, 52, 81, 69, 85, 89	⊢
	: , : , : , : , : , :
14	instantiation	20, 21, 22, 23	⊢
	: , : , :
15	instantiation	112, 34, 103	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	instantiation	112, 34, 107	⊢
	: , : , :
18	instantiation	24, 25, 26, 27, 28, 29, 30	⊢
	: , : , : , :
19	instantiation	92, 31, 32	⊢
	: , : , :
20	theorem		⊢
	proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
22	instantiation	33, 104	⊢
	: , :
23	instantiation	112, 34, 35	⊢
	: , : , :
24	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
26	instantiation	36	⊢
	: , : , : , : , :
27	instantiation	36	⊢
	: , : , : , : , :
28	instantiation	92, 37, 38	⊢
	: , : , :
29	instantiation	39, 83, 85, 40	⊢
	: , : , :
30	instantiation	39, 83, 89, 40	⊢
	: , : , :
31	instantiation	48, 79, 80, 41, 81, 52, 42, 85, 89	⊢
	: , : , : , : , : , :
32	instantiation	43, 44, 45, 46	⊢
	: , : , : , :
33	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
35	instantiation	47, 103, 107	⊢
	: , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
37	instantiation	48, 79, 80, 81, 52, 49, 85, 89, 50, 83	⊢
	: , : , : , : , : , :
38	instantiation	51, 80, 79, 52, 81, 85, 89, 83	⊢
	: , : , : , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
40	instantiation	53	⊢
	:
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
42	instantiation	54	⊢
	: , : , : , :
43	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
44	instantiation	92, 55, 56	⊢
	: , : , :
45	instantiation	78, 79, 104, 81, 57, 59, 85, 89, 58*	⊢
	: , : , : , : , : , :
46	instantiation	78, 114, 104, 79, 59, 81, 60, 89, 61*	⊢
	: , : , : , : , : , :
47	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
48	theorem		⊢
	proveit.numbers.addition.disassociation
49	instantiation	90	⊢
	: , :
50	instantiation	62, 83	⊢
	:
51	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
52	instantiation	90	⊢
	: , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
55	instantiation	64, 114, 104, 63, 85, 89	⊢
	: , : , : , : , : , : , :
56	instantiation	64, 80, 114, 65, 66, 85, 89	⊢
	: , : , : , : , : , : , :
57	instantiation	87	⊢
	: , : , :
58	instantiation	70, 67, 72*	⊢
	: , :
59	instantiation	87	⊢
	: , : , :
60	instantiation	68, 69, 85	⊢
	: , :
61	instantiation	70, 71, 72*	⊢
	: , :
62	theorem		⊢
	proveit.numbers.negation.complex_closure
63	instantiation	87	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.leftward_commutation
65	instantiation	90	⊢
	: , :
66	instantiation	90	⊢
	: , :
67	instantiation	75, 79, 104, 114, 81, 76, 83, 85, 73*	⊢
	: , : , : , : , : , :
68	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
69	instantiation	112, 97, 74	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.equality.equals_reversal
71	instantiation	75, 79, 104, 114, 81, 76, 83, 89, 77*	⊢
	: , : , : , : , : , :
72	instantiation	78, 79, 80, 114, 81, 82, 83, 84*	⊢
	: , : , : , : , : , :
73	instantiation	88, 85	⊢
	:
74	instantiation	112, 99, 86	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
76	instantiation	87	⊢
	: , : , :
77	instantiation	88, 89	⊢
	:
78	theorem		⊢
	proveit.numbers.addition.association
79	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
81	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
82	instantiation	90	⊢
	: , :
83	instantiation	112, 97, 91	⊢
	: , : , :
84	instantiation	92, 93, 94	⊢
	: , : , :
85	instantiation	112, 97, 95	⊢
	: , : , :
86	instantiation	112, 108, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
88	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
89	instantiation	112, 97, 98	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
91	instantiation	112, 99, 100	⊢
	: , : , :
92	axiom		⊢
	proveit.logic.equality.equals_transitivity
93	instantiation	101, 102	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
95	instantiation	105, 106, 103	⊢
	: , : , :
96	instantiation	112, 113, 104	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
98	instantiation	105, 106, 107	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
100	instantiation	112, 108, 109	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.substitution
102	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
103	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	110, 111	⊢
	: , :
107	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
109	instantiation	112, 113, 114	⊢
	: , : , :
110	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
112	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements