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