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, 126, 127, 4	⊢
	: , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
4	instantiation	6, 7, 8, 54, 9, 10*, 11*	⊢
	: , : , :
5	instantiation	35, 36, 12, 13	,  ⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	instantiation	135, 118, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
9	instantiation	15, 16	⊢
	: , :
10	instantiation	72, 17, 18	⊢
	: , : , :
11	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
12	instantiation	135, 115, 23	⊢
	: , : , :
13	instantiation	24, 36, 25, 26	,  ⊢
	: , : , : , :
14	instantiation	135, 121, 126	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.ordering.relax_less
16	instantiation	27, 137	⊢
	:
17	instantiation	39, 134, 120, 91, 40, 92, 28, 41, 46	⊢
	: , : , : , : , : , :
18	instantiation	29, 91, 120, 92, 40, 41, 46	⊢
	: , : , : , :
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	72, 30, 31	⊢
	: , : , :
21	instantiation	55	⊢
	:
22	instantiation	32, 33	⊢
	: , :
23	instantiation	135, 109, 34	⊢
	: , : , :
24	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
25	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
26	instantiation	35, 36, 37, 38	,  ⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
29	theorem		⊢
	proveit.numbers.addition.elim_zero_any
30	instantiation	39, 134, 120, 91, 40, 92, 43, 41, 46	⊢
	: , : , : , : , : , :
31	instantiation	42, 43, 46, 44	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.equals_reversal
33	instantiation	45, 46	⊢
	:
34	instantiation	47, 48, 69, 49	⊢
	: , :
35	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
36	instantiation	50, 98	⊢
	:
37	instantiation	106, 51, 52	,  ⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
39	theorem		⊢
	proveit.numbers.addition.disassociation
40	instantiation	102	⊢
	: , :
41	instantiation	135, 115, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
43	instantiation	135, 115, 54	⊢
	: , : , :
44	instantiation	55	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.elim_zero_left
46	instantiation	135, 115, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
48	instantiation	135, 87, 57	⊢
	: , : , :
49	instantiation	58, 59	⊢
	:
50	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
51	instantiation	135, 115, 60	⊢
	: , : , :
52	instantiation	79, 61, 62	,  ⊢
	: , : , :
53	instantiation	135, 118, 63	⊢
	: , : , :
54	instantiation	64, 65, 137	⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.equals_reflexivity
56	instantiation	135, 118, 66	⊢
	: , : , :
57	instantiation	135, 97, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
59	instantiation	135, 68, 69	⊢
	: , : , :
60	instantiation	135, 109, 70	⊢
	: , : , :
61	instantiation	99, 82, 71	,  ⊢
	: , :
62	instantiation	72, 73, 74	,  ⊢
	: , : , :
63	instantiation	135, 121, 129	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	75, 76	⊢
	: , :
66	instantiation	135, 121, 130	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
69	instantiation	77, 78	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
71	instantiation	79, 80, 81	,  ⊢
	: , : , :
72	axiom		⊢
	proveit.logic.equality.equals_transitivity
73	instantiation	90, 134, 83, 91, 85, 92, 82, 100, 101, 94	,  ⊢
	: , : , : , : , : , :
74	instantiation	90, 91, 120, 83, 92, 84, 85, 107, 86, 100, 101, 94	,  ⊢
	: , : , : , : , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
77	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
78	instantiation	135, 87, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.equality.sub_right_side_into
80	instantiation	99, 89, 94	,  ⊢
	: , :
81	instantiation	90, 91, 120, 134, 92, 93, 100, 101, 94	,  ⊢
	: , : , : , : , : , :
82	instantiation	135, 115, 95	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
84	instantiation	102	⊢
	: , :
85	instantiation	96	⊢
	: , : , :
86	instantiation	135, 115, 105	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
88	instantiation	135, 97, 98	⊢
	: , : , :
89	instantiation	99, 100, 101	,  ⊢
	: , :
90	theorem		⊢
	proveit.numbers.multiplication.disassociation
91	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
92	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
93	instantiation	102	⊢
	: , :
94	instantiation	135, 115, 103	⊢
	: , : , :
95	instantiation	104, 111, 105	⊢
	: , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
99	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
101	instantiation	106, 107, 108	,  ⊢
	: , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
103	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
104	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
105	instantiation	135, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
107	instantiation	135, 115, 111	⊢
	: , : , :
108	instantiation	112, 113	,  ⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
111	instantiation	135, 118, 114	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.negation.complex_closure
113	instantiation	135, 115, 116	,  ⊢
	: , : , :
114	instantiation	135, 121, 117	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
116	instantiation	135, 118, 119	,  ⊢
	: , : , :
117	instantiation	135, 133, 120	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
119	instantiation	135, 121, 122	,  ⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
121	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
122	instantiation	135, 123, 124	,  ⊢
	: , : , :
123	instantiation	125, 126, 127	⊢
	: , :
124	assumption		⊢
125	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
126	instantiation	128, 129, 130	⊢
	: , :
127	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
128	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
129	instantiation	131, 132	⊢
	:
130	instantiation	135, 133, 134	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.negation.int_closure
132	instantiation	135, 136, 137	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
137	assumption		⊢
*equality replacement requirements