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