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	modus ponens	1, 2	⊢
1	instantiation	3, 69, 70, 4	⊢
	: , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
4	instantiation	6, 7, 8, 56, 9, 10*, 11*	⊢
	: , : , :
5	instantiation	12, 13, 14, 15	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	81, 66, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
9	instantiation	17, 18	⊢
	: , :
10	instantiation	31, 19, 20	⊢
	: , : , :
11	instantiation	21, 22, 23, 24	⊢
	: , : , : , :
12	theorem		⊢
	proveit.linear_algebra.matrices.exponentiation.U_closure
13	instantiation	26, 41, 25	,  ⊢
	: , :
14	instantiation	26, 41, 27	⊢
	: , :
15	axiom		⊢
	proveit.physics.quantum.QPE._unitary_U
16	instantiation	81, 73, 69	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.ordering.relax_less
18	instantiation	28, 83	⊢
	:
19	instantiation	40, 80, 41, 42, 43, 44, 29, 45, 50	⊢
	: , : , : , : , : , :
20	instantiation	30, 42, 41, 44, 43, 45, 50	⊢
	: , : , : , :
21	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
22	instantiation	31, 32, 33	⊢
	: , : , :
23	instantiation	57	⊢
	:
24	instantiation	34, 35	⊢
	: , :
25	instantiation	36, 37	,  ⊢
	:
26	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
27	instantiation	81, 38, 39	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
30	theorem		⊢
	proveit.numbers.addition.elim_zero_any
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	40, 80, 41, 42, 43, 44, 47, 45, 50	⊢
	: , : , : , : , : , :
33	instantiation	46, 47, 50, 48	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.equals_reversal
35	instantiation	49, 50	⊢
	:
36	theorem		⊢
	proveit.numbers.negation.nat_closure
37	instantiation	51, 52, 53	,  ⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
39	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
40	theorem		⊢
	proveit.numbers.addition.disassociation
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
43	instantiation	54	⊢
	: , :
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	81, 58, 55	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
47	instantiation	81, 58, 56	⊢
	: , : , :
48	instantiation	57	⊢
	:
49	theorem		⊢
	proveit.numbers.addition.elim_zero_left
50	instantiation	81, 58, 59	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
52	instantiation	81, 60, 62	,  ⊢
	: , : , :
53	instantiation	61, 69, 70, 62	,  ⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55	instantiation	81, 66, 63	⊢
	: , : , :
56	instantiation	64, 65, 83	⊢
	: , : , :
57	axiom		⊢
	proveit.logic.equality.equals_reflexivity
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	81, 66, 67	⊢
	: , : , :
60	instantiation	68, 69, 70	⊢
	: , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
62	assumption		⊢
63	instantiation	81, 73, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	71, 72	⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	81, 73, 76	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
69	instantiation	74, 75, 76	⊢
	: , :
70	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
75	instantiation	77, 78	⊢
	:
76	instantiation	81, 79, 80	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.int_closure
78	instantiation	81, 82, 83	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
83	assumption		⊢
*equality replacement requirements