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	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
3	instantiation	8	⊢
	: , : , : , : , : , :
4	instantiation	8	⊢
	: , : , : , : , : , :
5	instantiation	36, 37, 33, 39	⊢
	: , : , :
6	instantiation	23, 9, 10	⊢
	: , : , :
7	reference	25	⊢
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
9	instantiation	11, 12	⊢
	: , : , :
10	instantiation	13, 14, 15, 16	⊢
	: , : , : , :
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	17, 33, 37	⊢
	: , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	20, 29, 30, 31, 21, 18, 33, 38, 19, 37	⊢
	: , : , : , : , : , :
15	instantiation	20, 30, 70, 21, 22, 33, 38, 27, 34, 37	⊢
	: , : , : , : , : , :
16	instantiation	23, 24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
18	instantiation	41	⊢
	: , :
19	instantiation	26, 27, 34	⊢
	: , :
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	instantiation	41	⊢
	: , :
22	instantiation	41	⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	28, 29, 70, 30, 31, 32, 33, 38, 34, 37, 35	⊢
	: , : , : , : , : , : , : , :
25	instantiation	36, 37, 38, 39	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
27	instantiation	68, 45, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	41	⊢
	: , :
33	instantiation	68, 45, 42	⊢
	: , : , :
34	instantiation	68, 45, 43	⊢
	: , : , :
35	instantiation	47	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
37	instantiation	68, 45, 44	⊢
	: , : , :
38	instantiation	68, 45, 46	⊢
	: , : , :
39	instantiation	47	⊢
	:
40	instantiation	68, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	53, 54, 67	⊢
	: , : , :
43	instantiation	68, 51, 50	⊢
	: , : , :
44	instantiation	68, 51, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	53, 54, 55	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_reflexivity
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
49	instantiation	68, 56, 57	⊢
	: , : , :
50	instantiation	68, 59, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	68, 59, 65	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
54	instantiation	60, 61	⊢
	: , :
55	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
57	instantiation	68, 62, 63	⊢
	: , : , :
58	instantiation	64, 65	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
63	instantiation	66, 67	⊢
	:
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.int_neg_closure
67	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1