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