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	27	⊢
2	instantiation	5, 6, 7, 8, 9, 10, 11, 15*, 18*	⊢
	: , : , : , :
3	instantiation	60	⊢
	:
4	instantiation	12, 13	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	instantiation	55	⊢
	: , :
8	instantiation	55	⊢
	: , :
9	instantiation	55	⊢
	: , :
10	instantiation	16, 14, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	19, 20	⊢
	: , :
14	instantiation	80, 23, 79	⊢
	: , : , :
15	instantiation	51, 58, 48, 53	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	instantiation	80, 23, 67	⊢
	: , : , :
18	instantiation	38, 21, 22	⊢
	: , : , :
19	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
20	instantiation	80, 23, 24	⊢
	: , : , :
21	instantiation	25, 26	⊢
	: , : , :
22	instantiation	27, 28, 29, 30	⊢
	: , : , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
24	instantiation	31, 79, 67	⊢
	: , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	32, 48, 58	⊢
	: , :
27	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
28	instantiation	35, 44, 45, 46, 36, 33, 48, 52, 34, 58	⊢
	: , : , : , : , : , :
29	instantiation	35, 45, 82, 36, 37, 48, 52, 42, 49, 58	⊢
	: , : , : , : , : , :
30	instantiation	38, 39, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
32	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
33	instantiation	55	⊢
	: , :
34	instantiation	41, 42, 49	⊢
	: , :
35	theorem		⊢
	proveit.numbers.addition.disassociation
36	instantiation	55	⊢
	: , :
37	instantiation	55	⊢
	: , :
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	43, 44, 82, 45, 46, 47, 48, 52, 49, 58, 50	⊢
	: , : , : , : , : , : , : , :
40	instantiation	51, 58, 52, 53	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
42	instantiation	80, 63, 54	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
44	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
46	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
47	instantiation	55	⊢
	: , :
48	instantiation	80, 63, 56	⊢
	: , : , :
49	instantiation	57, 58	⊢
	:
50	instantiation	60	⊢
	:
51	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
52	instantiation	80, 63, 59	⊢
	: , : , :
53	instantiation	60	⊢
	:
54	instantiation	80, 61, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	instantiation	65, 66, 79	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.negation.complex_closure
58	instantiation	80, 63, 64	⊢
	: , : , :
59	instantiation	65, 66, 67	⊢
	: , : , :
60	axiom		⊢
	proveit.logic.equality.equals_reflexivity
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
62	instantiation	80, 68, 69	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	80, 70, 71	⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
66	instantiation	72, 73	⊢
	: , :
67	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
69	instantiation	80, 74, 75	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	80, 76, 77	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
75	instantiation	78, 79	⊢
	:
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	80, 81, 82	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.negation.int_neg_closure
79	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
80	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements