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	, ,  ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.logic.booleans.disjunction.disassociate
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	25	⊢
4	reference	63	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	reference	17	⊢
7	instantiation	8, 9, 10, 11	, ,  ⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_left
9	instantiation	13, 66, 17, 12	⊢
	: , :
10	instantiation	13, 43, 14, 15	⊢
	: , :
11	instantiation	16, 66, 17, 18	, ,  ⊢
	: , :
12	modus ponens	19, 20	⊢
13	theorem		⊢
	proveit.logic.booleans.disjunction.closure
14	instantiation	24, 21	⊢
	: , :
15	modus ponens	22, 23	⊢
16	theorem		⊢
	proveit.logic.booleans.disjunction.any_if_all
17	instantiation	24, 25	⊢
	: , :
18	modus ponens	26, 27	, ,  ⊢
19	instantiation	33, 59, 60, 34	⊢
	: , : , : , :
20	generalization	28	⊢
21	instantiation	64, 32, 43	⊢
	: , : , :
22	instantiation	33, 59, 29, 30	⊢
	: , : , : , :
23	generalization	31	⊢
24	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
25	instantiation	64, 32, 66	⊢
	: , : , :
26	instantiation	33, 59, 60, 34	⊢
	: , : , : , :
27	generalization	35	, ,  ⊢
28	instantiation	37	⊢
	: , :
29	instantiation	64, 65, 43	⊢
	: , : , :
30	instantiation	38, 36	⊢
	:
31	instantiation	37	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
33	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
34	instantiation	38, 39	⊢
	:
35	instantiation	40, 41, 42	, , ,  ⊢
	: , : , : , :
36	instantiation	44, 43, 45	⊢
	: , :
37	theorem		⊢
	proveit.logic.equality.not_equals_is_bool
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
39	instantiation	44, 66, 45	⊢
	: , :
40	theorem		⊢
	proveit.physics.quantum.circuits.qcircuit_output_part_neq
41	instantiation	46, 47, 48	⊢
	:
42	instantiation	49, 66, 50, 51, 52	, ,  ⊢
	: , : , :
43	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
44	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
47	instantiation	64, 53, 61	⊢
	: , : , :
48	instantiation	54, 55, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_neq
50	assumption		⊢
51	assumption		⊢
52	assumption		⊢
53	instantiation	57, 59, 60	⊢
	: , :
54	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
55	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
56	instantiation	58, 59, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
58	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
59	instantiation	64, 62, 63	⊢
	: , : , :
60	instantiation	64, 65, 66	⊢
	: , : , :
61	assumption		⊢
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
66	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos