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