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	50	⊢
2	instantiation	5, 6, 7, 8, 9, 10, 11, 12, 13, 14*	⊢
	: , : , : , :
3	instantiation	78, 15	⊢
	: , :
4	instantiation	78, 16	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
7	instantiation	38	⊢
	: , : , : , : , :
8	instantiation	38	⊢
	: , : , : , : , :
9	instantiation	38	⊢
	: , : , : , : , :
10	instantiation	19, 17, 30	⊢
	: , : , :
11	instantiation	19, 18, 70	⊢
	: , : , :
12	instantiation	19, 18, 31	⊢
	: , : , :
13	instantiation	19, 25, 32	⊢
	: , : , :
14	instantiation	111, 20, 21	⊢
	: , : , :
15	instantiation	91, 143, 96, 95, 67, 97, 77, 104, 108	⊢
	: , : , : , : , : , :
16	instantiation	22, 23, 24, 25	⊢
	: , : , :
17	instantiation	141, 36, 140	⊢
	: , : , :
18	instantiation	141, 36, 131	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.equality.sub_left_side_into
20	instantiation	26, 27, 28, 29, 30, 70, 31, 32	⊢
	: , : , : , :
21	instantiation	111, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.core_expr_types.tuples.len_of_ranges_with_repeated_indices_from_1
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	instantiation	35, 128	⊢
	: , :
25	instantiation	141, 36, 37	⊢
	: , : , :
26	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
28	instantiation	38	⊢
	: , : , : , : , :
29	instantiation	38	⊢
	: , : , : , : , :
30	instantiation	87, 99, 104, 88	⊢
	: , : , :
31	instantiation	111, 39, 40	⊢
	: , : , :
32	instantiation	111, 41, 42	⊢
	: , : , :
33	instantiation	66, 43, 96, 95, 44, 67, 97, 104, 108	⊢
	: , : , : , : , : , :
34	instantiation	50, 45, 46, 47	⊢
	: , : , : , :
35	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
37	instantiation	48, 140, 131	⊢
	: , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
39	instantiation	123, 49	⊢
	: , : , :
40	instantiation	50, 51, 52, 53	⊢
	: , : , : , :
41	instantiation	66, 95, 96, 97, 67, 84, 104, 108, 85, 99	⊢
	: , : , : , : , : , :
42	instantiation	54, 96, 95, 67, 97, 104, 108, 99	⊢
	: , : , : , : , : , : , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
44	instantiation	55	⊢
	: , : , : , :
45	instantiation	111, 56, 57	⊢
	: , : , :
46	instantiation	94, 95, 128, 97, 58, 60, 104, 108, 59*	⊢
	: , : , : , : , : , :
47	instantiation	94, 143, 128, 95, 60, 97, 61, 108, 62*	⊢
	: , : , : , : , : , :
48	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
49	instantiation	63, 104, 99	⊢
	: , :
50	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
51	instantiation	66, 95, 96, 97, 67, 64, 104, 108, 65, 99	⊢
	: , : , : , : , : , :
52	instantiation	66, 96, 143, 67, 68, 104, 108, 82, 85, 99	⊢
	: , : , : , : , : , :
53	instantiation	111, 69, 70	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
56	instantiation	72, 143, 128, 71, 104, 108	⊢
	: , : , : , : , : , : , :
57	instantiation	72, 96, 143, 73, 74, 104, 108	⊢
	: , : , : , : , : , : , :
58	instantiation	106	⊢
	: , : , :
59	instantiation	78, 75, 80*	⊢
	: , :
60	instantiation	106	⊢
	: , : , :
61	instantiation	76, 77, 104	⊢
	: , :
62	instantiation	78, 79, 80*	⊢
	: , :
63	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
64	instantiation	109	⊢
	: , :
65	instantiation	81, 82, 85	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.disassociation
67	instantiation	109	⊢
	: , :
68	instantiation	109	⊢
	: , :
69	instantiation	83, 95, 143, 96, 97, 84, 104, 108, 85, 99, 86	⊢
	: , : , : , : , : , : , : , :
70	instantiation	87, 99, 108, 88	⊢
	: , : , :
71	instantiation	106	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.leftward_commutation
73	instantiation	109	⊢
	: , :
74	instantiation	109	⊢
	: , :
75	instantiation	91, 95, 128, 143, 97, 92, 99, 104, 89*	⊢
	: , : , : , : , : , :
76	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
77	instantiation	141, 119, 90	⊢
	: , : , :
78	theorem		⊢
	proveit.logic.equality.equals_reversal
79	instantiation	91, 95, 128, 143, 97, 92, 99, 108, 93*	⊢
	: , : , : , : , : , :
80	instantiation	94, 95, 96, 143, 97, 98, 99, 100*	⊢
	: , : , : , : , : , :
81	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
82	instantiation	141, 119, 101	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
84	instantiation	109	⊢
	: , :
85	instantiation	141, 119, 102	⊢
	: , : , :
86	instantiation	103	⊢
	:
87	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
88	instantiation	103	⊢
	:
89	instantiation	107, 104	⊢
	:
90	instantiation	141, 121, 105	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
92	instantiation	106	⊢
	: , : , :
93	instantiation	107, 108	⊢
	:
94	theorem		⊢
	proveit.numbers.addition.association
95	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
97	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
98	instantiation	109	⊢
	: , :
99	instantiation	141, 119, 110	⊢
	: , : , :
100	instantiation	111, 112, 113	⊢
	: , : , :
101	instantiation	141, 114, 115	⊢
	: , : , :
102	instantiation	141, 121, 116	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.equals_reflexivity
104	instantiation	141, 119, 117	⊢
	: , : , :
105	instantiation	141, 132, 118	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
107	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
108	instantiation	141, 119, 120	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
110	instantiation	141, 121, 122	⊢
	: , : , :
111	axiom		⊢
	proveit.logic.equality.equals_transitivity
112	instantiation	123, 124	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
115	instantiation	141, 125, 126	⊢
	: , : , :
116	instantiation	141, 132, 127	⊢
	: , : , :
117	instantiation	129, 130, 140	⊢
	: , : , :
118	instantiation	141, 142, 128	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
120	instantiation	129, 130, 131	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
122	instantiation	141, 132, 136	⊢
	: , : , :
123	axiom		⊢
	proveit.logic.equality.substitution
124	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
126	instantiation	141, 133, 134	⊢
	: , : , :
127	instantiation	135, 136	⊢
	:
128	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
129	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
130	instantiation	137, 138	⊢
	: , :
131	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
134	instantiation	139, 140	⊢
	:
135	theorem		⊢
	proveit.numbers.negation.int_closure
136	instantiation	141, 142, 143	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
139	theorem		⊢
	proveit.numbers.negation.int_neg_closure
140	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
141	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
142	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements