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	⊢
	: , : , :
1	reference	160	⊢
2	instantiation	4, 214, 5, 6, 7*	⊢
	: , : , :
3	instantiation	8, 214, 9, 10, 11, 12	⊢
	: , : , : , :
4	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
5	instantiation	66, 13, 135, 20	⊢
	: , : , : , :
6	instantiation	18, 203, 204, 175, 31	⊢
	: , : , :
7	instantiation	14, 15, 184, 28, 16*, 28*	⊢
	: , :
8	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
9	instantiation	66, 17, 135, 20	⊢
	: , : , : , :
10	instantiation	18, 203, 204, 96, 31	⊢
	: , : , :
11	instantiation	66, 19, 135, 20	⊢
	: , : , : , :
12	modus ponens	21, 22	⊢
13	instantiation	150, 23, 28	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_rev
15	instantiation	99, 197, 166, 24, 167, 56, 211, 100	⊢
	: , : , : , : , :
16	instantiation	92, 25	⊢
	: , :
17	instantiation	150, 26, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
19	instantiation	150, 27, 28	⊢
	: , : , :
20	instantiation	92, 29	⊢
	: , :
21	instantiation	30, 203, 204, 31	⊢
	: , : , : , :
22	generalization	32	⊢
23	instantiation	37, 38	⊢
	: , : , :
24	instantiation	179	⊢
	: , :
25	instantiation	33, 206, 34, 35, 36	⊢
	: , : , : , : , : , :
26	instantiation	37, 38	⊢
	: , : , :
27	instantiation	37, 38	⊢
	: , : , :
28	instantiation	141, 39, 40	⊢
	: , : , :
29	instantiation	41, 42	⊢
	: , :
30	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
31	instantiation	119, 43, 44, 146, 45, 46*, 47*	⊢
	: , : , :
32	instantiation	95, 96, 48, 49	,  ⊢
	: , : , : , :
33	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
34	instantiation	50, 51, 56	⊢
	: , :
35	instantiation	92, 52	⊢
	: , :
36	instantiation	92, 53	⊢
	: , :
37	theorem		⊢
	proveit.core_expr_types.tuples.range_len
38	instantiation	54, 154, 55, 166, 56, 211	⊢
	: , :
39	instantiation	103, 57	⊢
	: , : , :
40	instantiation	66, 58, 59, 60	⊢
	: , : , : , :
41	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
42	instantiation	212, 73, 214	⊢
	: , : , :
43	instantiation	212, 195, 61	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
45	instantiation	62, 63	⊢
	: , :
46	instantiation	141, 64, 65	⊢
	: , : , :
47	instantiation	66, 67, 86, 68	⊢
	: , : , : , :
48	instantiation	212, 192, 69	⊢
	: , : , :
49	instantiation	70, 96, 71, 72	,  ⊢
	: , : , : , :
50	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
51	instantiation	212, 73, 74	⊢
	: , : , :
52	instantiation	141, 75, 76	⊢
	: , : , :
53	instantiation	141, 77, 78	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.add_nat_closure
55	instantiation	171	⊢
	: , : , :
56	instantiation	79, 80	⊢
	:
57	instantiation	81, 132, 131, 104*	⊢
	: , :
58	instantiation	115, 211, 197, 82, 88, 134, 84, 131	⊢
	: , : , : , : , : , :
59	instantiation	89, 166, 154, 167, 83, 134, 84, 131	⊢
	: , : , : , :
60	instantiation	85, 131, 134, 86	⊢
	: , : , :
61	instantiation	212, 198, 203	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.ordering.relax_less
63	instantiation	87, 214	⊢
	:
64	instantiation	115, 211, 197, 166, 116, 167, 88, 132, 131	⊢
	: , : , : , : , : , :
65	instantiation	89, 166, 197, 167, 116, 132, 131	⊢
	: , : , : , :
66	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
67	instantiation	141, 90, 91	⊢
	: , : , :
68	instantiation	92, 93	⊢
	: , :
69	instantiation	212, 186, 94	⊢
	: , : , :
70	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
71	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
72	instantiation	95, 96, 97, 98	,  ⊢
	: , : , : , :
73	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
74	instantiation	99, 211, 166, 167, 100	⊢
	: , : , : , : , :
75	instantiation	103, 104	⊢
	: , : , :
76	instantiation	141, 101, 102	⊢
	: , : , :
77	instantiation	103, 104	⊢
	: , : , :
78	instantiation	108, 134	⊢
	:
79	theorem		⊢
	proveit.numbers.negation.nat_closure
80	instantiation	105, 203, 106	⊢
	:
81	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
82	instantiation	179	⊢
	: , :
83	instantiation	171	⊢
	: , : , :
84	instantiation	189, 131	⊢
	:
85	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
86	instantiation	147	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
89	theorem		⊢
	proveit.numbers.addition.elim_zero_any
90	instantiation	115, 211, 197, 166, 116, 167, 134, 132, 131	⊢
	: , : , : , : , : , :
91	instantiation	107, 134, 131, 135	⊢
	: , : , :
92	theorem		⊢
	proveit.logic.equality.equals_reversal
93	instantiation	108, 131	⊢
	:
94	instantiation	109, 110, 138, 111	⊢
	: , :
95	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
96	instantiation	112, 175	⊢
	:
97	instantiation	183, 113, 114	,  ⊢
	: , :
98	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
99	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
100	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
101	instantiation	115, 166, 197, 211, 167, 116, 132, 131, 134	⊢
	: , : , : , : , : , :
102	instantiation	117, 134, 131, 135	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.substitution
104	instantiation	118, 134	⊢
	:
105	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
106	instantiation	119, 145, 144, 146, 120, 121*, 122*	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
108	theorem		⊢
	proveit.numbers.addition.elim_zero_left
109	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
110	instantiation	212, 162, 123	⊢
	: , : , :
111	instantiation	124, 125	⊢
	:
112	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
113	instantiation	212, 192, 126	⊢
	: , : , :
114	instantiation	150, 127, 128	,  ⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.addition.disassociation
116	instantiation	179	⊢
	: , :
117	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
118	theorem		⊢
	proveit.numbers.negation.double_negation
119	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
120	instantiation	129, 214	⊢
	:
121	instantiation	130, 131, 132	⊢
	: , :
122	instantiation	133, 134, 135	⊢
	: , :
123	instantiation	212, 174, 136	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
125	instantiation	212, 137, 138	⊢
	: , : , :
126	instantiation	212, 186, 139	⊢
	: , : , :
127	instantiation	176, 153, 140	,  ⊢
	: , :
128	instantiation	141, 142, 143	,  ⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
130	theorem		⊢
	proveit.numbers.addition.commutation
131	instantiation	212, 192, 144	⊢
	: , : , :
132	instantiation	212, 192, 145	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
134	instantiation	212, 192, 146	⊢
	: , : , :
135	instantiation	147	⊢
	:
136	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
138	instantiation	148, 149	⊢
	:
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
140	instantiation	150, 151, 152	,  ⊢
	: , : , :
141	axiom		⊢
	proveit.logic.equality.equals_transitivity
142	instantiation	165, 211, 154, 166, 156, 167, 153, 177, 178, 169	,  ⊢
	: , : , : , : , : , :
143	instantiation	165, 166, 197, 154, 167, 155, 156, 184, 157, 177, 178, 169	,  ⊢
	: , : , : , : , : , :
144	instantiation	212, 195, 158	⊢
	: , : , :
145	instantiation	212, 195, 159	⊢
	: , : , :
146	instantiation	160, 161, 214	⊢
	: , : , :
147	axiom		⊢
	proveit.logic.equality.equals_reflexivity
148	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
149	instantiation	212, 162, 163	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.equality.sub_right_side_into
151	instantiation	176, 164, 169	,  ⊢
	: , :
152	instantiation	165, 166, 197, 211, 167, 168, 177, 178, 169	,  ⊢
	: , : , : , : , : , :
153	instantiation	212, 192, 170	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
155	instantiation	179	⊢
	: , :
156	instantiation	171	⊢
	: , : , :
157	instantiation	212, 192, 182	⊢
	: , : , :
158	instantiation	212, 198, 207	⊢
	: , : , :
159	instantiation	212, 198, 206	⊢
	: , : , :
160	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
161	instantiation	172, 173	⊢
	: , :
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
163	instantiation	212, 174, 175	⊢
	: , : , :
164	instantiation	176, 177, 178	,  ⊢
	: , :
165	theorem		⊢
	proveit.numbers.multiplication.disassociation
166	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
167	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
168	instantiation	179	⊢
	: , :
169	instantiation	212, 192, 180	⊢
	: , : , :
170	instantiation	181, 188, 182	⊢
	: , :
171	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
172	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
173	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
174	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
175	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
176	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
177	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
178	instantiation	183, 184, 185	,  ⊢
	: , :
179	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
180	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
181	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
182	instantiation	212, 186, 187	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
184	instantiation	212, 192, 188	⊢
	: , : , :
185	instantiation	189, 190	,  ⊢
	:
186	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
187	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
188	instantiation	212, 195, 191	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.negation.complex_closure
190	instantiation	212, 192, 193	,  ⊢
	: , : , :
191	instantiation	212, 198, 194	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
193	instantiation	212, 195, 196	,  ⊢
	: , : , :
194	instantiation	212, 210, 197	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
196	instantiation	212, 198, 199	,  ⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
198	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
199	instantiation	212, 200, 201	,  ⊢
	: , : , :
200	instantiation	202, 203, 204	⊢
	: , :
201	assumption		⊢
202	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
203	instantiation	205, 206, 207	⊢
	: , :
204	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
205	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
206	instantiation	208, 209	⊢
	:
207	instantiation	212, 210, 211	⊢
	: , : , :
208	theorem		⊢
	proveit.numbers.negation.int_closure
209	instantiation	212, 213, 214	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
211	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
212	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
213	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
214	assumption		⊢
*equality replacement requirements