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, 7, 8, 9*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.general_len
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
3	instantiation	25	⊢
	: , : , : , : , : , :
4	instantiation	25	⊢
	: , : , : , : , : , :
5	instantiation	25	⊢
	: , : , : , : , : , :
6	instantiation	11, 10, 20	⊢
	: , : , :
7	instantiation	11, 12, 57	⊢
	: , : , :
8	instantiation	11, 12, 21	⊢
	: , : , :
9	instantiation	82, 13, 14	⊢
	: , : , :
10	instantiation	115, 15, 114	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.sub_left_side_into
12	instantiation	115, 15, 102	⊢
	: , : , :
13	instantiation	16, 17, 18, 19, 20, 57, 21	⊢
	: , : , : , :
14	instantiation	36, 22, 23, 24	⊢
	: , : , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
16	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
18	instantiation	25	⊢
	: , : , : , : , : , :
19	instantiation	25	⊢
	: , : , : , : , : , :
20	instantiation	75, 88, 77, 76	⊢
	: , : , :
21	instantiation	82, 26, 27	⊢
	: , : , :
22	instantiation	82, 28, 29	⊢
	: , : , :
23	instantiation	63, 69, 99, 71, 30, 32, 77, 81, 31*	⊢
	: , : , : , : , : , :
24	instantiation	63, 117, 99, 69, 32, 71, 33, 81, 34*	⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
26	instantiation	93, 35	⊢
	: , : , :
27	instantiation	36, 37, 38, 39	⊢
	: , : , : , :
28	instantiation	41, 117, 99, 40, 77, 81	⊢
	: , : , : , : , : , : , :
29	instantiation	41, 70, 117, 42, 43, 77, 81	⊢
	: , : , : , : , : , : , :
30	instantiation	79	⊢
	: , : , :
31	instantiation	47, 44, 49*	⊢
	: , :
32	instantiation	79	⊢
	: , : , :
33	instantiation	45, 46, 77	⊢
	: , :
34	instantiation	47, 48, 49*	⊢
	: , :
35	instantiation	50, 77, 88	⊢
	: , :
36	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
37	instantiation	53, 69, 70, 71, 54, 51, 77, 81, 52, 88	⊢
	: , : , : , : , : , :
38	instantiation	53, 70, 117, 54, 55, 77, 81, 67, 73, 88	⊢
	: , : , : , : , : , :
39	instantiation	82, 56, 57	⊢
	: , : , :
40	instantiation	79	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.leftward_commutation
42	instantiation	86	⊢
	: , :
43	instantiation	86	⊢
	: , :
44	instantiation	60, 69, 99, 117, 71, 61, 88, 77, 58*	⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
46	instantiation	115, 97, 59	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.equals_reversal
48	instantiation	60, 69, 99, 117, 71, 61, 88, 81, 62*	⊢
	: , : , : , : , : , :
49	instantiation	63, 69, 70, 117, 71, 64, 88, 65*	⊢
	: , : , : , : , : , :
50	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
51	instantiation	86	⊢
	: , :
52	instantiation	66, 67, 73	⊢
	: , :
53	theorem		⊢
	proveit.numbers.addition.disassociation
54	instantiation	86	⊢
	: , :
55	instantiation	86	⊢
	: , :
56	instantiation	68, 69, 117, 70, 71, 72, 77, 81, 73, 88, 74	⊢
	: , : , : , : , : , : , : , :
57	instantiation	75, 88, 81, 76	⊢
	: , : , :
58	instantiation	80, 77	⊢
	:
59	instantiation	115, 105, 78	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
61	instantiation	79	⊢
	: , : , :
62	instantiation	80, 81	⊢
	:
63	theorem		⊢
	proveit.numbers.addition.association
64	instantiation	86	⊢
	: , :
65	instantiation	82, 83, 84	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
67	instantiation	115, 97, 85	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
72	instantiation	86	⊢
	: , :
73	instantiation	87, 88	⊢
	:
74	instantiation	89	⊢
	:
75	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
76	instantiation	89	⊢
	:
77	instantiation	115, 97, 90	⊢
	: , : , :
78	instantiation	115, 111, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
81	instantiation	115, 97, 92	⊢
	: , : , :
82	axiom		⊢
	proveit.logic.equality.equals_transitivity
83	instantiation	93, 94	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
85	instantiation	115, 95, 96	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
87	theorem		⊢
	proveit.numbers.negation.complex_closure
88	instantiation	115, 97, 98	⊢
	: , : , :
89	axiom		⊢
	proveit.logic.equality.equals_reflexivity
90	instantiation	100, 101, 114	⊢
	: , : , :
91	instantiation	115, 116, 99	⊢
	: , : , :
92	instantiation	100, 101, 102	⊢
	: , : , :
93	axiom		⊢
	proveit.logic.equality.substitution
94	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
96	instantiation	115, 103, 104	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
98	instantiation	115, 105, 106	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
100	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
101	instantiation	107, 108	⊢
	: , :
102	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
104	instantiation	115, 109, 110	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
106	instantiation	115, 111, 112	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
110	instantiation	113, 114	⊢
	:
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
112	instantiation	115, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.negation.int_neg_closure
114	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
115	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements