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