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	43	⊢
2	instantiation	7, 4	,  ⊢
	: , : , :
3	instantiation	5, 6	,  ⊢
	: , :
4	instantiation	7, 8	,  ⊢
	: , : , :
5	theorem		⊢
	proveit.physics.quantum.circuits.unary_multi_output_reduction
6	instantiation	9, 10, 11	,  ⊢
	:
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	43, 12, 13	,  ⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
10	instantiation	92, 80, 96	,  ⊢
	: , :
11	instantiation	14, 61, 25, 15, 16, 17*, 18*	,  ⊢
	: , : , :
12	instantiation	47, 54, 19, 81, 55, 20, 51, 21, 59, 36	,  ⊢
	: , : , : , : , : , :
13	instantiation	22, 81, 54, 55, 51, 36, 59	,  ⊢
	: , : , : , : , : , : , : , :
14	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
15	instantiation	99, 84, 23	,  ⊢
	: , : , :
16	instantiation	24, 25, 65, 79, 26, 27	,  ⊢
	: , : , :
17	instantiation	31, 28, 29, 30	⊢
	: , : , : , :
18	instantiation	31, 32, 33, 34	,  ⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
20	instantiation	35	⊢
	: , : , :
21	instantiation	63, 36	⊢
	:
22	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
23	instantiation	99, 88, 37	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
25	instantiation	99, 84, 38	⊢
	: , : , :
26	instantiation	39, 90, 91, 87	,  ⊢
	: , : , :
27	instantiation	40, 41	⊢
	:
28	instantiation	47, 54, 98, 81, 55, 42, 56, 64, 46	⊢
	: , : , : , : , : , :
29	instantiation	47, 98, 54, 42, 49, 55, 56, 64, 59, 50	⊢
	: , : , : , : , : , :
30	instantiation	43, 44, 45	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	47, 54, 98, 81, 55, 48, 51, 64, 46	,  ⊢
	: , : , : , : , : , :
33	instantiation	47, 98, 54, 48, 49, 55, 51, 64, 59, 50	,  ⊢
	: , : , : , : , : , :
34	instantiation	53, 81, 54, 55, 51, 64, 59, 57	,  ⊢
	: , : , : , : , : , : , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36	instantiation	99, 72, 52	⊢
	: , : , :
37	instantiation	92, 80, 94	,  ⊢
	: , :
38	instantiation	99, 88, 90	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	instantiation	62	⊢
	: , :
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	53, 81, 54, 55, 56, 64, 59, 57	⊢
	: , : , : , : , : , : , : , :
45	instantiation	58, 59, 60	⊢
	: , :
46	instantiation	99, 72, 61	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.disassociation
48	instantiation	62	⊢
	: , :
49	instantiation	62	⊢
	: , :
50	instantiation	63, 64	⊢
	:
51	instantiation	99, 72, 65	,  ⊢
	: , : , :
52	instantiation	99, 84, 66	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
54	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
55	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
56	instantiation	99, 72, 67	⊢
	: , : , :
57	instantiation	68	⊢
	:
58	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
59	instantiation	99, 72, 70	⊢
	: , : , :
60	instantiation	68	⊢
	:
61	instantiation	69, 70, 71	⊢
	: , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.numbers.negation.complex_closure
64	instantiation	99, 72, 79	⊢
	: , : , :
65	instantiation	99, 84, 73	,  ⊢
	: , : , :
66	instantiation	99, 88, 74	⊢
	: , : , :
67	instantiation	99, 84, 75	⊢
	: , : , :
68	axiom		⊢
	proveit.logic.equality.equals_reflexivity
69	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
70	instantiation	76, 77, 101	⊢
	: , : , :
71	instantiation	78, 79	⊢
	:
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	instantiation	99, 88, 80	,  ⊢
	: , : , :
74	instantiation	99, 97, 81	⊢
	: , : , :
75	instantiation	99, 88, 93	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
77	instantiation	82, 83	⊢
	: , :
78	theorem		⊢
	proveit.numbers.negation.real_closure
79	instantiation	99, 84, 85	⊢
	: , : , :
80	instantiation	99, 86, 87	,  ⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
82	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
85	instantiation	99, 88, 94	⊢
	: , : , :
86	instantiation	89, 90, 91	⊢
	: , :
87	assumption		⊢
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
89	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
90	instantiation	92, 93, 94	⊢
	: , :
91	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
92	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
93	instantiation	95, 96	⊢
	:
94	instantiation	99, 97, 98	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	99, 100, 101	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
101	assumption		⊢
*equality replacement requirements