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, 122, 123, 4	⊢
	: , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
4	instantiation	6, 7, 8, 58, 9, 10*, 11*	⊢
	: , : , :
5	instantiation	39, 40, 12, 13	,  ⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	131, 114, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
9	instantiation	15, 16	⊢
	: , :
10	instantiation	76, 17, 18	⊢
	: , : , :
11	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
12	instantiation	23, 50, 24, 25	⊢
	: , :
13	instantiation	26, 40, 27, 28	,  ⊢
	: , : , : , :
14	instantiation	131, 117, 122	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.ordering.relax_less
16	instantiation	29, 133	⊢
	:
17	instantiation	43, 130, 116, 90, 44, 91, 30, 45, 50	⊢
	: , : , : , : , : , :
18	instantiation	31, 90, 116, 91, 44, 45, 50	⊢
	: , : , : , :
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	76, 32, 33	⊢
	: , : , :
21	instantiation	59	⊢
	:
22	instantiation	34, 35	⊢
	: , :
23	theorem		⊢
	proveit.numbers.division.div_complex_closure
24	instantiation	36, 103	⊢
	:
25	instantiation	37, 53, 38	⊢
	: , :
26	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
27	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
28	instantiation	39, 40, 41, 42	,  ⊢
	: , : , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	theorem		⊢
	proveit.numbers.addition.elim_zero_any
32	instantiation	43, 130, 116, 90, 44, 91, 47, 45, 50	⊢
	: , : , : , : , : , :
33	instantiation	46, 47, 50, 48	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.equals_reversal
35	instantiation	49, 50	⊢
	:
36	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
37	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
38	instantiation	51, 52, 53	⊢
	: , :
39	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
40	instantiation	54, 73	⊢
	:
41	instantiation	102, 55, 56	,  ⊢
	: , :
42	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
43	theorem		⊢
	proveit.numbers.addition.disassociation
44	instantiation	99	⊢
	: , :
45	instantiation	131, 111, 57	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
47	instantiation	131, 111, 58	⊢
	: , : , :
48	instantiation	59	⊢
	:
49	theorem		⊢
	proveit.numbers.addition.elim_zero_left
50	instantiation	131, 111, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
52	instantiation	131, 62, 61	⊢
	: , : , :
53	instantiation	131, 62, 63	⊢
	: , : , :
54	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
55	instantiation	131, 111, 64	⊢
	: , : , :
56	instantiation	81, 65, 66	,  ⊢
	: , : , :
57	instantiation	131, 114, 67	⊢
	: , : , :
58	instantiation	68, 69, 133	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_reflexivity
60	instantiation	131, 114, 70	⊢
	: , : , :
61	instantiation	131, 72, 71	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
63	instantiation	131, 72, 73	⊢
	: , : , :
64	instantiation	131, 105, 74	⊢
	: , : , :
65	instantiation	96, 84, 75	,  ⊢
	: , :
66	instantiation	76, 77, 78	,  ⊢
	: , : , :
67	instantiation	131, 117, 125	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
69	instantiation	79, 80	⊢
	: , :
70	instantiation	131, 117, 126	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
75	instantiation	81, 82, 83	,  ⊢
	: , : , :
76	axiom		⊢
	proveit.logic.equality.equals_transitivity
77	instantiation	89, 130, 85, 90, 87, 91, 84, 97, 98, 93	,  ⊢
	: , : , : , : , : , :
78	instantiation	89, 90, 116, 85, 91, 86, 87, 103, 94, 97, 98, 93	,  ⊢
	: , : , : , : , : , :
79	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
81	theorem		⊢
	proveit.logic.equality.sub_right_side_into
82	instantiation	96, 88, 93	,  ⊢
	: , :
83	instantiation	89, 90, 116, 130, 91, 92, 97, 98, 93	,  ⊢
	: , : , : , : , : , :
84	instantiation	96, 103, 94	⊢
	: , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
86	instantiation	99	⊢
	: , :
87	instantiation	95	⊢
	: , : , :
88	instantiation	96, 97, 98	,  ⊢
	: , :
89	theorem		⊢
	proveit.numbers.multiplication.disassociation
90	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
91	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
92	instantiation	99	⊢
	: , :
93	instantiation	131, 111, 100	⊢
	: , : , :
94	instantiation	131, 111, 101	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
96	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
98	instantiation	102, 103, 104	,  ⊢
	: , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
100	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
101	instantiation	131, 105, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
103	instantiation	131, 111, 107	⊢
	: , : , :
104	instantiation	108, 109	,  ⊢
	:
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
107	instantiation	131, 114, 110	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.negation.complex_closure
109	instantiation	131, 111, 112	,  ⊢
	: , : , :
110	instantiation	131, 117, 113	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	instantiation	131, 114, 115	,  ⊢
	: , : , :
113	instantiation	131, 129, 116	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
115	instantiation	131, 117, 118	,  ⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
118	instantiation	131, 119, 120	,  ⊢
	: , : , :
119	instantiation	121, 122, 123	⊢
	: , :
120	assumption		⊢
121	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
122	instantiation	124, 125, 126	⊢
	: , :
123	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
124	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
125	instantiation	127, 128	⊢
	:
126	instantiation	131, 129, 130	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	instantiation	131, 132, 133	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
133	assumption		⊢
*equality replacement requirements