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