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