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	,  ⊢
	: , :
1	theorem		⊢
	proveit.physics.quantum.circuits.unary_multi_output_reduction
2	instantiation	3, 4, 5	,  ⊢
	:
3	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
4	instantiation	75, 64, 79	,  ⊢
	: , :
5	instantiation	6, 47, 13, 7, 8, 9*, 10*	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
7	instantiation	82, 67, 11	,  ⊢
	: , : , :
8	instantiation	12, 13, 51, 63, 14, 15	,  ⊢
	: , : , :
9	instantiation	19, 16, 17, 18	⊢
	: , : , : , :
10	instantiation	19, 20, 21, 22	,  ⊢
	: , : , : , :
11	instantiation	82, 71, 23	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
13	instantiation	82, 67, 24	⊢
	: , : , :
14	instantiation	25, 73, 74, 70	,  ⊢
	: , : , :
15	instantiation	26, 27	⊢
	:
16	instantiation	33, 40, 81, 39, 41, 28, 42, 50, 32	⊢
	: , : , : , : , : , :
17	instantiation	33, 81, 40, 28, 35, 41, 42, 50, 45, 36	⊢
	: , : , : , : , : , :
18	instantiation	29, 30, 31	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	33, 40, 81, 39, 41, 34, 37, 50, 32	,  ⊢
	: , : , : , : , : , :
21	instantiation	33, 81, 40, 34, 35, 41, 37, 50, 45, 36	,  ⊢
	: , : , : , : , : , :
22	instantiation	38, 39, 40, 41, 37, 50, 45, 43	,  ⊢
	: , : , : , : , : , : , : , :
23	instantiation	75, 64, 77	,  ⊢
	: , :
24	instantiation	82, 71, 73	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	instantiation	48	⊢
	: , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	38, 39, 40, 41, 42, 50, 45, 43	⊢
	: , : , : , : , : , : , : , :
31	instantiation	44, 45, 46	⊢
	: , :
32	instantiation	82, 57, 47	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.disassociation
34	instantiation	48	⊢
	: , :
35	instantiation	48	⊢
	: , :
36	instantiation	49, 50	⊢
	:
37	instantiation	82, 57, 51	,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
40	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
41	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42	instantiation	82, 57, 52	⊢
	: , : , :
43	instantiation	53	⊢
	:
44	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
45	instantiation	82, 57, 55	⊢
	: , : , :
46	instantiation	53	⊢
	:
47	instantiation	54, 55, 56	⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49	theorem		⊢
	proveit.numbers.negation.complex_closure
50	instantiation	82, 57, 63	⊢
	: , : , :
51	instantiation	82, 67, 58	,  ⊢
	: , : , :
52	instantiation	82, 67, 59	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
55	instantiation	60, 61, 84	⊢
	: , : , :
56	instantiation	62, 63	⊢
	:
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	82, 71, 64	,  ⊢
	: , : , :
59	instantiation	82, 71, 76	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
61	instantiation	65, 66	⊢
	: , :
62	theorem		⊢
	proveit.numbers.negation.real_closure
63	instantiation	82, 67, 68	⊢
	: , : , :
64	instantiation	82, 69, 70	,  ⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	82, 71, 77	⊢
	: , : , :
69	instantiation	72, 73, 74	⊢
	: , :
70	assumption		⊢
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
73	instantiation	75, 76, 77	⊢
	: , :
74	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
75	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
76	instantiation	78, 79	⊢
	:
77	instantiation	82, 80, 81	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.negation.int_closure
79	instantiation	82, 83, 84	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
82	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
84	assumption		⊢
*equality replacement requirements