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	, ,  ⊢
	: , : , : , : , : , :
1	reference	9	⊢
2	reference	30	⊢
3	reference	26	⊢
4	reference	10	⊢
5	reference	22	⊢
6	reference	19	⊢
7	reference	11	⊢
8	instantiation	9, 10, 30, 68, 11, 22, 12	, ,  ⊢
	: , : , : , : , : , :
9	theorem		⊢
	proveit.logic.booleans.disjunction.disassociate
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	13, 14, 15, 16	, ,  ⊢
	: , :
13	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_left
14	instantiation	18, 71, 22, 17	⊢
	: , :
15	instantiation	18, 48, 19, 20	⊢
	: , :
16	instantiation	21, 71, 22, 23	, ,  ⊢
	: , :
17	modus ponens	24, 25	⊢
18	theorem		⊢
	proveit.logic.booleans.disjunction.closure
19	instantiation	29, 26	⊢
	: , :
20	modus ponens	27, 28	⊢
21	theorem		⊢
	proveit.logic.booleans.disjunction.any_if_all
22	instantiation	29, 30	⊢
	: , :
23	modus ponens	31, 32	, ,  ⊢
24	instantiation	38, 64, 65, 39	⊢
	: , : , : , :
25	generalization	33	⊢
26	instantiation	69, 37, 48	⊢
	: , : , :
27	instantiation	38, 64, 34, 35	⊢
	: , : , : , :
28	generalization	36	⊢
29	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
30	instantiation	69, 37, 71	⊢
	: , : , :
31	instantiation	38, 64, 65, 39	⊢
	: , : , : , :
32	generalization	40	, ,  ⊢
33	instantiation	42	⊢
	: , :
34	instantiation	69, 70, 48	⊢
	: , : , :
35	instantiation	43, 41	⊢
	:
36	instantiation	42	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
38	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
39	instantiation	43, 44	⊢
	:
40	instantiation	45, 46, 47	, , ,  ⊢
	: , : , : , :
41	instantiation	49, 48, 50	⊢
	: , :
42	theorem		⊢
	proveit.logic.equality.not_equals_is_bool
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
44	instantiation	49, 71, 50	⊢
	: , :
45	theorem		⊢
	proveit.physics.quantum.circuits.qcircuit_output_part_neq
46	instantiation	51, 52, 53	⊢
	:
47	instantiation	54, 71, 55, 56, 57	, ,  ⊢
	: , : , :
48	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
49	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
51	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
52	instantiation	69, 58, 66	⊢
	: , : , :
53	instantiation	59, 60, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_neq
55	assumption		⊢
56	assumption		⊢
57	assumption		⊢
58	instantiation	62, 64, 65	⊢
	: , :
59	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
60	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
61	instantiation	63, 64, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
63	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
64	instantiation	69, 67, 68	⊢
	: , : , :
65	instantiation	69, 70, 71	⊢
	: , : , :
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
71	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos