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	modus ponens	1, 2	⊢
1	instantiation	3, 85, 23, 4	⊢
	: , : , : , : , : , : , : , :
2	instantiation	5, 6	⊢
	: , :
3	theorem		⊢
	proveit.physics.quantum.circuits.circuit_equiv_temporal_sub
4	instantiation	29, 7, 68, 8	⊢
	: , : , : , :
5	theorem		⊢
	proveit.physics.quantum.circuits.equiv_reversal
6	instantiation	9, 10, 90, 11	⊢
	: , : , :
7	instantiation	12, 13, 14	⊢
	: , : , :
8	instantiation	15, 16	⊢
	: , :
9	axiom		⊢
	proveit.physics.quantum.QPE.QPE1_def
10	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
11	axiom		⊢
	proveit.physics.quantum.QPE._unitary_U
12	theorem		⊢
	proveit.logic.equality.sub_right_side_into
13	instantiation	17, 18	⊢
	: , : , :
14	instantiation	19, 20, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.equals_reversal
16	instantiation	22, 23	⊢
	: , :
17	theorem		⊢
	proveit.core_expr_types.tuples.range_len
18	instantiation	24, 44, 25, 43, 26, 85	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	27, 28	⊢
	: , : , :
21	instantiation	29, 30, 31, 32	⊢
	: , : , : , :
22	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
23	instantiation	88, 33, 90	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_nat_closure
25	instantiation	55	⊢
	: , : , :
26	instantiation	34, 35	⊢
	:
27	axiom		⊢
	proveit.logic.equality.substitution
28	instantiation	36, 65, 64, 37*	⊢
	: , :
29	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
30	instantiation	38, 85, 39, 40, 41, 67, 47, 64	⊢
	: , : , : , : , : , :
31	instantiation	42, 43, 44, 45, 46, 67, 47, 64	⊢
	: , : , : , :
32	instantiation	48, 64, 67, 49	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
34	theorem		⊢
	proveit.numbers.negation.nat_closure
35	instantiation	50, 51, 52	⊢
	:
36	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
37	instantiation	53, 67	⊢
	:
38	theorem		⊢
	proveit.numbers.addition.disassociation
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	instantiation	54	⊢
	: , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
42	theorem		⊢
	proveit.numbers.addition.elim_zero_any
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
45	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
46	instantiation	55	⊢
	: , : , :
47	instantiation	56, 64	⊢
	:
48	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
49	instantiation	73	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
51	instantiation	57, 81, 79	⊢
	: , :
52	instantiation	58, 70, 69, 72, 59, 60*, 61*	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.double_negation
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
56	theorem		⊢
	proveit.numbers.negation.complex_closure
57	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
58	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
59	instantiation	62, 90	⊢
	:
60	instantiation	63, 64, 65	⊢
	: , :
61	instantiation	66, 67, 68	⊢
	: , :
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
63	theorem		⊢
	proveit.numbers.addition.commutation
64	instantiation	88, 71, 69	⊢
	: , : , :
65	instantiation	88, 71, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
67	instantiation	88, 71, 72	⊢
	: , : , :
68	instantiation	73	⊢
	:
69	instantiation	88, 75, 74	⊢
	: , : , :
70	instantiation	88, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	77, 78, 90	⊢
	: , : , :
73	axiom		⊢
	proveit.logic.equality.equals_reflexivity
74	instantiation	88, 80, 79	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	88, 80, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
78	instantiation	82, 83	⊢
	: , :
79	instantiation	88, 84, 85	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
81	instantiation	86, 87	⊢
	:
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.integers.nat_within_int
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
86	theorem		⊢
	proveit.numbers.negation.int_closure
87	instantiation	88, 89, 90	⊢
	: , : , :
88	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
90	assumption		⊢
*equality replacement requirements