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, 124, 125, 4	⊢
	: , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
4	instantiation	6, 7, 103, 57, 8, 9*, 10*	⊢
	: , : , :
5	instantiation	38, 39, 11, 12	,  ⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	133, 116, 13	⊢
	: , : , :
8	instantiation	14, 15	⊢
	: , :
9	instantiation	73, 16, 17	⊢
	: , : , :
10	instantiation	18, 19, 20, 21	⊢
	: , : , : , :
11	instantiation	22, 49, 23, 24	⊢
	: , :
12	instantiation	25, 39, 26, 27	,  ⊢
	: , : , : , :
13	instantiation	133, 119, 124	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.relax_less
15	instantiation	28, 135	⊢
	:
16	instantiation	42, 132, 118, 87, 43, 88, 29, 44, 49	⊢
	: , : , : , : , : , :
17	instantiation	30, 87, 118, 88, 43, 44, 49	⊢
	: , : , : , :
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	73, 31, 32	⊢
	: , : , :
20	instantiation	58	⊢
	:
21	instantiation	33, 34	⊢
	: , :
22	theorem		⊢
	proveit.numbers.division.div_complex_closure
23	instantiation	35, 100	⊢
	:
24	instantiation	36, 52, 37	⊢
	: , :
25	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
26	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
27	instantiation	38, 39, 40, 41	,  ⊢
	: , : , : , :
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	instantiation	42, 132, 118, 87, 43, 88, 46, 44, 49	⊢
	: , : , : , : , : , :
32	instantiation	45, 46, 49, 47	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.equals_reversal
34	instantiation	48, 49	⊢
	:
35	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
36	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
37	instantiation	50, 51, 52	⊢
	: , :
38	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
39	instantiation	53, 70	⊢
	:
40	instantiation	99, 54, 55	,  ⊢
	: , :
41	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
42	theorem		⊢
	proveit.numbers.addition.disassociation
43	instantiation	96	⊢
	: , :
44	instantiation	133, 113, 56	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
46	instantiation	133, 113, 57	⊢
	: , : , :
47	instantiation	58	⊢
	:
48	theorem		⊢
	proveit.numbers.addition.elim_zero_left
49	instantiation	133, 113, 104	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
51	instantiation	133, 60, 59	⊢
	: , : , :
52	instantiation	133, 60, 61	⊢
	: , : , :
53	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
54	instantiation	133, 113, 62	⊢
	: , : , :
55	instantiation	78, 63, 64	,  ⊢
	: , : , :
56	instantiation	133, 116, 65	⊢
	: , : , :
57	instantiation	66, 67, 135	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.equals_reflexivity
59	instantiation	133, 69, 68	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	133, 69, 70	⊢
	: , : , :
62	instantiation	133, 106, 71	⊢
	: , : , :
63	instantiation	93, 81, 72	,  ⊢
	: , :
64	instantiation	73, 74, 75	,  ⊢
	: , : , :
65	instantiation	133, 119, 127	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
67	instantiation	76, 77	⊢
	: , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
72	instantiation	78, 79, 80	,  ⊢
	: , : , :
73	axiom		⊢
	proveit.logic.equality.equals_transitivity
74	instantiation	86, 132, 82, 87, 84, 88, 81, 94, 95, 90	,  ⊢
	: , : , : , : , : , :
75	instantiation	86, 87, 118, 82, 88, 83, 84, 100, 91, 94, 95, 90	,  ⊢
	: , : , : , : , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78	theorem		⊢
	proveit.logic.equality.sub_right_side_into
79	instantiation	93, 85, 90	,  ⊢
	: , :
80	instantiation	86, 87, 118, 132, 88, 89, 94, 95, 90	,  ⊢
	: , : , : , : , : , :
81	instantiation	93, 100, 91	⊢
	: , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
83	instantiation	96	⊢
	: , :
84	instantiation	92	⊢
	: , : , :
85	instantiation	93, 94, 95	,  ⊢
	: , :
86	theorem		⊢
	proveit.numbers.multiplication.disassociation
87	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	96	⊢
	: , :
90	instantiation	133, 113, 97	⊢
	: , : , :
91	instantiation	133, 113, 98	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
93	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
95	instantiation	99, 100, 101	,  ⊢
	: , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
97	instantiation	102, 103, 104, 105	⊢
	: , : , :
98	instantiation	133, 106, 107	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
100	instantiation	133, 113, 108	⊢
	: , : , :
101	instantiation	109, 110	,  ⊢
	:
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
104	instantiation	133, 116, 111	⊢
	: , : , :
105	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
108	instantiation	133, 116, 112	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.negation.complex_closure
110	instantiation	133, 113, 114	,  ⊢
	: , : , :
111	instantiation	133, 119, 128	⊢
	: , : , :
112	instantiation	133, 119, 115	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	instantiation	133, 116, 117	,  ⊢
	: , : , :
115	instantiation	133, 131, 118	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
117	instantiation	133, 119, 120	,  ⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
120	instantiation	133, 121, 122	,  ⊢
	: , : , :
121	instantiation	123, 124, 125	⊢
	: , :
122	assumption		⊢
123	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
124	instantiation	126, 127, 128	⊢
	: , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
126	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
127	instantiation	129, 130	⊢
	:
128	instantiation	133, 131, 132	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.negation.int_closure
130	instantiation	133, 134, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
133	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
135	assumption		⊢
*equality replacement requirements