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, 114, 117, 77, 4, 78	⊢
	: , : , : , : , : , : , : , :
2	instantiation	5, 6, 7, 83, 48, 8, 9, 10, 11, 12, 13, 14, 15, 16, 44, 77, 30, 17, 18, 41*	⊢
	: , : , : , : , : , :
3	theorem		⊢
	proveit.physics.quantum.circuits.circuit_equiv_temporal_sub
4	instantiation	90	⊢
	: , :
5	theorem		⊢
	proveit.physics.quantum.circuits.output_consolidation
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	instantiation	90	⊢
	: , :
8	instantiation	90	⊢
	: , :
9	instantiation	19, 20	⊢
	: , :
10	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
11	instantiation	26, 21, 22, 23	⊢
	: , : , : , :
12	instantiation	49, 24	⊢
	: , :
13	instantiation	90	⊢
	: , :
14	instantiation	49, 25	⊢
	: , :
15	instantiation	26, 27, 28, 29	⊢
	: , : , : , :
16	instantiation	55, 80, 104, 41	⊢
	: , : , :
17	instantiation	54, 30, 31	⊢
	: , :
18	instantiation	32, 73, 33, 34, 35, 36	⊢
	: , :
19	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
20	instantiation	37, 83	⊢
	:
21	instantiation	38	⊢
	: , : , :
22	instantiation	51	⊢
	:
23	instantiation	49, 39	⊢
	: , :
24	instantiation	40, 43, 41	⊢
	: , : , :
25	instantiation	42, 43, 44	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
27	instantiation	45	⊢
	: , :
28	instantiation	51	⊢
	:
29	instantiation	49, 46	⊢
	: , :
30	instantiation	115, 47, 83	⊢
	: , : , :
31	instantiation	115, 47, 48	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
33	instantiation	86	⊢
	: , : , :
34	instantiation	51	⊢
	:
35	instantiation	49, 50	⊢
	: , :
36	instantiation	51	⊢
	:
37	theorem		⊢
	proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
39	instantiation	56, 52, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
41	instantiation	59, 104	⊢
	:
42	theorem		⊢
	proveit.core_expr_types.tuples.partition_back
43	instantiation	54, 114, 75	⊢
	: , :
44	instantiation	55, 104, 102, 93	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2
46	instantiation	56, 57, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
48	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
49	theorem		⊢
	proveit.logic.equality.equals_reversal
50	instantiation	59, 60	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	instantiation	64, 61	⊢
	: , : , :
53	instantiation	91, 62, 63	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
55	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
56	theorem		⊢
	proveit.logic.equality.sub_right_side_into
57	instantiation	64, 65	⊢
	: , : , :
58	instantiation	91, 66, 67	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.elim_zero_left
60	instantiation	115, 106, 68	⊢
	: , : , :
61	instantiation	72, 73, 69, 114, 75, 117	⊢
	: , :
62	instantiation	100, 99	⊢
	: , : , :
63	instantiation	76, 77, 114, 117, 78, 70, 102, 80, 104, 71*	⊢
	: , : , : , : , : , :
64	theorem		⊢
	proveit.core_expr_types.tuples.range_len
65	instantiation	72, 73, 74, 117, 75	⊢
	: , :
66	instantiation	100, 99	⊢
	: , : , :
67	instantiation	76, 77, 114, 117, 78, 79, 104, 80, 81*	⊢
	: , : , : , : , : , :
68	instantiation	87, 82, 83	⊢
	: , : , :
69	instantiation	86	⊢
	: , : , :
70	instantiation	90	⊢
	: , :
71	instantiation	91, 84, 85	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.add_nat_closure
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
74	instantiation	86	⊢
	: , : , :
75	instantiation	87, 88, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.addition.association
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	90	⊢
	: , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
81	instantiation	91, 92, 93	⊢
	: , : , :
82	instantiation	96, 94	⊢
	: , :
83	assumption		⊢
84	instantiation	100, 95	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
86	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
87	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
88	instantiation	96, 97	⊢
	: , :
89	instantiation	98, 99	⊢
	: , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
91	axiom		⊢
	proveit.logic.equality.equals_transitivity
92	instantiation	100, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
95	instantiation	103, 102	⊢
	:
96	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
97	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
98	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
99	theorem		⊢
	proveit.numbers.negation.negated_zero
100	axiom		⊢
	proveit.logic.equality.substitution
101	instantiation	103, 104	⊢
	:
102	instantiation	115, 106, 105	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.addition.elim_zero_right
104	instantiation	115, 106, 107	⊢
	: , : , :
105	instantiation	115, 109, 108	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
107	instantiation	115, 109, 110	⊢
	: , : , :
108	instantiation	115, 112, 111	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
110	instantiation	115, 112, 113	⊢
	: , : , :
111	instantiation	115, 116, 114	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
113	instantiation	115, 116, 117	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
115	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements