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	, ,  ⊢
	: , : , :
1	theorem		⊢
	proveit.core_expr_types.expr_arrays.varray_neq_via_any_elem_neq
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
3	instantiation	6	⊢
	: , : , : , :
4	instantiation	6	⊢
	: , : , : , :
5	instantiation	7, 8, 45, 9, 46, 10, 11, 12, 13, 14	, ,  ⊢
	: , : , : , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
7	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_any
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
9	instantiation	15	⊢
	: , : , :
10	instantiation	101	⊢
	: , :
11	instantiation	101	⊢
	: , :
12	instantiation	101	⊢
	: , :
13	instantiation	101	⊢
	: , :
14	instantiation	16, 17, 18, 19, 20, 21	, ,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_neq_via_any_elem_neq
17	instantiation	108, 22, 23	⊢
	: , :
18	instantiation	24, 25, 26	⊢
	: , : , :
19	instantiation	28, 27, 30, 31	⊢
	: , : , : , :
20	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
21	instantiation	44, 82, 78, 45, 69, 66, 46, 32	, ,  ⊢
	: , : , : , : , : , :
22	instantiation	50, 130, 49	⊢
	: , : , :
23	instantiation	50, 107, 51	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	33, 49	⊢
	: , : , :
26	instantiation	33, 51	⊢
	: , : , :
27	instantiation	35, 36, 34, 38, 39, 40, 41, 49*, 51*	⊢
	: , : , : , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	35, 36, 37, 38, 39, 40, 41, 49*, 51*	⊢
	: , : , : , :
30	instantiation	75	⊢
	:
31	instantiation	42, 43	⊢
	: , :
32	instantiation	44, 45, 82, 127, 46, 69, 47	, ,  ⊢
	: , : , : , : , : , :
33	axiom		⊢
	proveit.logic.equality.substitution
34	instantiation	48	⊢
	: , :
35	theorem		⊢
	proveit.core_expr_types.tuples.general_len
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	instantiation	48	⊢
	: , :
38	instantiation	48	⊢
	: , :
39	instantiation	48	⊢
	: , :
40	instantiation	50, 82, 49	⊢
	: , : , :
41	instantiation	50, 78, 51	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.equals_reversal
43	instantiation	52, 53	⊢
	: , :
44	theorem		⊢
	proveit.logic.booleans.disjunction.disassociate
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
47	instantiation	54, 55, 56, 57	, ,  ⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49	instantiation	59, 60, 58, 62	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.equality.sub_left_side_into
51	instantiation	59, 60, 61, 62	⊢
	: , : , :
52	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
53	instantiation	128, 93, 63	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_left
55	instantiation	65, 130, 69, 64	⊢
	: , :
56	instantiation	65, 107, 66, 67	⊢
	: , :
57	instantiation	68, 130, 69, 70	, ,  ⊢
	: , :
58	instantiation	128, 73, 71	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
60	instantiation	128, 73, 72	⊢
	: , : , :
61	instantiation	128, 73, 74	⊢
	: , : , :
62	instantiation	75	⊢
	:
63	instantiation	108, 130, 107	⊢
	: , :
64	modus ponens	76, 77	⊢
65	theorem		⊢
	proveit.logic.booleans.disjunction.closure
66	instantiation	81, 78	⊢
	: , :
67	modus ponens	79, 80	⊢
68	theorem		⊢
	proveit.logic.booleans.disjunction.any_if_all
69	instantiation	81, 82	⊢
	: , :
70	modus ponens	83, 84	, ,  ⊢
71	instantiation	87, 88, 130	⊢
	: , : , :
72	instantiation	128, 85, 86	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	87, 88, 107	⊢
	: , : , :
75	axiom		⊢
	proveit.logic.equality.equals_reflexivity
76	instantiation	94, 123, 124, 95	⊢
	: , : , : , :
77	generalization	89	⊢
78	instantiation	128, 93, 107	⊢
	: , : , :
79	instantiation	94, 123, 90, 91	⊢
	: , : , : , :
80	generalization	92	⊢
81	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
82	instantiation	128, 93, 130	⊢
	: , : , :
83	instantiation	94, 123, 124, 95	⊢
	: , : , : , :
84	generalization	96	, ,  ⊢
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	128, 97, 123	⊢
	: , : , :
87	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
88	instantiation	98, 99	⊢
	: , :
89	instantiation	101	⊢
	: , :
90	instantiation	128, 129, 107	⊢
	: , : , :
91	instantiation	102, 100	⊢
	:
92	instantiation	101	⊢
	: , :
93	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
94	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
95	instantiation	102, 103	⊢
	:
96	instantiation	104, 105, 106	, , ,  ⊢
	: , : , : , :
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
98	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
100	instantiation	108, 107, 109	⊢
	: , :
101	theorem		⊢
	proveit.logic.equality.not_equals_is_bool
102	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
103	instantiation	108, 130, 109	⊢
	: , :
104	theorem		⊢
	proveit.physics.quantum.circuits.qcircuit_output_part_neq
105	instantiation	110, 111, 112	⊢
	:
106	instantiation	113, 130, 114, 115, 116	, ,  ⊢
	: , : , :
107	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
108	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
110	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
111	instantiation	128, 117, 125	⊢
	: , : , :
112	instantiation	118, 119, 120	⊢
	: , : , :
113	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_neq
114	assumption		⊢
115	assumption		⊢
116	assumption		⊢
117	instantiation	121, 123, 124	⊢
	: , :
118	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
119	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
120	instantiation	122, 123, 124, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
122	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
123	instantiation	128, 126, 127	⊢
	: , : , :
124	instantiation	128, 129, 130	⊢
	: , : , :
125	assumption		⊢
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
130	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
*equality replacement requirements