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, 30	⊢
	: , : , :
12	instantiation	17, 18, 70	⊢
	: , : , :
13	instantiation	96, 19, 20	⊢
	: , : , :
14	instantiation	73, 133, 83, 82, 67, 84, 59, 91, 95	⊢
	: , : , : , : , : , :
15	instantiation	21, 22, 23, 24	⊢
	: , : , :
16	instantiation	131, 35, 130	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_left_side_into
18	instantiation	131, 35, 118	⊢
	: , : , :
19	instantiation	25, 26, 27, 28, 29, 30, 70	⊢
	: , : , : , :
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, 115	⊢
	: , :
24	instantiation	131, 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, 89, 91, 90	⊢
	: , : , :
30	instantiation	96, 38, 39	⊢
	: , : , :
31	instantiation	96, 40, 41	⊢
	: , : , :
32	instantiation	76, 82, 115, 84, 42, 44, 91, 95, 43*	⊢
	: , : , : , : , : , :
33	instantiation	76, 133, 115, 82, 44, 84, 45, 95, 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, 130, 118	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
38	instantiation	108, 48	⊢
	: , : , :
39	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
40	instantiation	54, 133, 115, 53, 91, 95	⊢
	: , : , : , : , : , : , :
41	instantiation	54, 83, 133, 55, 56, 91, 95	⊢
	: , : , : , : , : , : , :
42	instantiation	93	⊢
	: , : , :
43	instantiation	60, 57, 62*	⊢
	: , :
44	instantiation	93	⊢
	: , : , :
45	instantiation	58, 59, 91	⊢
	: , :
46	instantiation	60, 61, 62*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
48	instantiation	63, 91, 89	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	66, 82, 83, 84, 67, 64, 91, 95, 65, 89	⊢
	: , : , : , : , : , :
51	instantiation	66, 83, 133, 67, 68, 91, 95, 80, 86, 89	⊢
	: , : , : , : , : , :
52	instantiation	96, 69, 70	⊢
	: , : , :
53	instantiation	93	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.leftward_commutation
55	instantiation	100	⊢
	: , :
56	instantiation	100	⊢
	: , :
57	instantiation	73, 82, 115, 133, 84, 74, 89, 91, 71*	⊢
	: , : , : , : , : , :
58	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
59	instantiation	131, 106, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.equality.equals_reversal
61	instantiation	73, 82, 115, 133, 84, 74, 89, 95, 75*	⊢
	: , : , : , : , : , :
62	instantiation	76, 82, 83, 133, 84, 77, 89, 78*	⊢
	: , : , : , : , : , :
63	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
64	instantiation	100	⊢
	: , :
65	instantiation	79, 80, 86	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.disassociation
67	instantiation	100	⊢
	: , :
68	instantiation	100	⊢
	: , :
69	instantiation	81, 82, 133, 83, 84, 85, 91, 95, 86, 89, 87	⊢
	: , : , : , : , : , : , : , :
70	instantiation	88, 89, 95, 90	⊢
	: , : , :
71	instantiation	94, 91	⊢
	:
72	instantiation	131, 113, 92	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
74	instantiation	93	⊢
	: , : , :
75	instantiation	94, 95	⊢
	:
76	theorem		⊢
	proveit.numbers.addition.association
77	instantiation	100	⊢
	: , :
78	instantiation	96, 97, 98	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
80	instantiation	131, 106, 99	⊢
	: , : , :
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	100	⊢
	: , :
86	instantiation	131, 106, 101	⊢
	: , : , :
87	instantiation	103	⊢
	:
88	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
89	instantiation	131, 106, 102	⊢
	: , : , :
90	instantiation	103	⊢
	:
91	instantiation	131, 106, 104	⊢
	: , : , :
92	instantiation	131, 122, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
94	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
95	instantiation	131, 106, 107	⊢
	: , : , :
96	axiom		⊢
	proveit.logic.equality.equals_transitivity
97	instantiation	108, 109	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
99	instantiation	131, 110, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	instantiation	131, 113, 112	⊢
	: , : , :
102	instantiation	131, 113, 114	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.equals_reflexivity
104	instantiation	116, 117, 130	⊢
	: , : , :
105	instantiation	131, 132, 115	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
107	instantiation	116, 117, 118	⊢
	: , : , :
108	axiom		⊢
	proveit.logic.equality.substitution
109	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
111	instantiation	131, 119, 120	⊢
	: , : , :
112	instantiation	131, 122, 121	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	131, 122, 128	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
116	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
117	instantiation	123, 124	⊢
	: , :
118	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
120	instantiation	131, 125, 126	⊢
	: , : , :
121	instantiation	127, 128	⊢
	:
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
123	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
126	instantiation	129, 130	⊢
	:
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	instantiation	131, 132, 133	⊢
	: , : , :
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