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	49	⊢
2	instantiation	5, 6, 7, 8, 9, 10, 11, 12, 13*	⊢
	: , : , : , :
3	instantiation	60, 14	⊢
	: , :
4	instantiation	60, 15	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
7	instantiation	37	⊢
	: , : , : , : , : , :
8	instantiation	37	⊢
	: , : , : , : , : , :
9	instantiation	37	⊢
	: , : , : , : , : , :
10	instantiation	17, 16, 29	⊢
	: , : , :
11	instantiation	17, 18, 70	⊢
	: , : , :
12	instantiation	17, 18, 30	⊢
	: , : , :
13	instantiation	95, 19, 20	⊢
	: , : , :
14	instantiation	73, 130, 83, 82, 67, 84, 59, 90, 94	⊢
	: , : , : , : , : , :
15	instantiation	21, 22, 23, 24	⊢
	: , : , :
16	instantiation	128, 35, 127	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_left_side_into
18	instantiation	128, 35, 115	⊢
	: , : , :
19	instantiation	25, 26, 27, 28, 29, 70, 30	⊢
	: , : , : , :
20	instantiation	49, 31, 32, 33	⊢
	: , : , : , :
21	theorem		⊢
	proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
23	instantiation	34, 112	⊢
	: , :
24	instantiation	128, 35, 36	⊢
	: , : , :
25	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
27	instantiation	37	⊢
	: , : , : , : , : , :
28	instantiation	37	⊢
	: , : , : , : , : , :
29	instantiation	88, 101, 90, 89	⊢
	: , : , :
30	instantiation	95, 38, 39	⊢
	: , : , :
31	instantiation	95, 40, 41	⊢
	: , : , :
32	instantiation	76, 82, 112, 84, 42, 44, 90, 94, 43*	⊢
	: , : , : , : , : , :
33	instantiation	76, 130, 112, 82, 44, 84, 45, 94, 46*	⊢
	: , : , : , : , : , :
34	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
36	instantiation	47, 127, 115	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
38	instantiation	106, 48	⊢
	: , : , :
39	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
40	instantiation	54, 130, 112, 53, 90, 94	⊢
	: , : , : , : , : , : , :
41	instantiation	54, 83, 130, 55, 56, 90, 94	⊢
	: , : , : , : , : , : , :
42	instantiation	92	⊢
	: , : , :
43	instantiation	60, 57, 62*	⊢
	: , :
44	instantiation	92	⊢
	: , : , :
45	instantiation	58, 59, 90	⊢
	: , :
46	instantiation	60, 61, 62*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
48	instantiation	63, 90, 101	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	66, 82, 83, 84, 67, 64, 90, 94, 65, 101	⊢
	: , : , : , : , : , :
51	instantiation	66, 83, 130, 67, 68, 90, 94, 80, 86, 101	⊢
	: , : , : , : , : , :
52	instantiation	95, 69, 70	⊢
	: , : , :
53	instantiation	92	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.leftward_commutation
55	instantiation	99	⊢
	: , :
56	instantiation	99	⊢
	: , :
57	instantiation	73, 82, 112, 130, 84, 74, 101, 90, 71*	⊢
	: , : , : , : , : , :
58	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
59	instantiation	128, 110, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.equality.equals_reversal
61	instantiation	73, 82, 112, 130, 84, 74, 101, 94, 75*	⊢
	: , : , : , : , : , :
62	instantiation	76, 82, 83, 130, 84, 77, 101, 78*	⊢
	: , : , : , : , : , :
63	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
64	instantiation	99	⊢
	: , :
65	instantiation	79, 80, 86	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.disassociation
67	instantiation	99	⊢
	: , :
68	instantiation	99	⊢
	: , :
69	instantiation	81, 82, 130, 83, 84, 85, 90, 94, 86, 101, 87	⊢
	: , : , : , : , : , : , : , :
70	instantiation	88, 101, 94, 89	⊢
	: , : , :
71	instantiation	93, 90	⊢
	:
72	instantiation	128, 118, 91	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
74	instantiation	92	⊢
	: , : , :
75	instantiation	93, 94	⊢
	:
76	theorem		⊢
	proveit.numbers.addition.association
77	instantiation	99	⊢
	: , :
78	instantiation	95, 96, 97	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
80	instantiation	128, 110, 98	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
82	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
84	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
85	instantiation	99	⊢
	: , :
86	instantiation	100, 101	⊢
	:
87	instantiation	102	⊢
	:
88	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
89	instantiation	102	⊢
	:
90	instantiation	128, 110, 103	⊢
	: , : , :
91	instantiation	128, 124, 104	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
93	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
94	instantiation	128, 110, 105	⊢
	: , : , :
95	axiom		⊢
	proveit.logic.equality.equals_transitivity
96	instantiation	106, 107	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
98	instantiation	128, 108, 109	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
100	theorem		⊢
	proveit.numbers.negation.complex_closure
101	instantiation	128, 110, 111	⊢
	: , : , :
102	axiom		⊢
	proveit.logic.equality.equals_reflexivity
103	instantiation	113, 114, 127	⊢
	: , : , :
104	instantiation	128, 129, 112	⊢
	: , : , :
105	instantiation	113, 114, 115	⊢
	: , : , :
106	axiom		⊢
	proveit.logic.equality.substitution
107	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
109	instantiation	128, 116, 117	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
111	instantiation	128, 118, 119	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
113	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
114	instantiation	120, 121	⊢
	: , :
115	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
117	instantiation	128, 122, 123	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
119	instantiation	128, 124, 125	⊢
	: , : , :
120	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
123	instantiation	126, 127	⊢
	:
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
125	instantiation	128, 129, 130	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.negation.int_neg_closure
127	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements