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*, 4*, 5*	⊢
	: , : , :
1	reference	114	⊢
2	modus ponens	6, 7	⊢
3	instantiation	8, 183	⊢
	: , :
4	instantiation	8, 183	⊢
	: , :
5	instantiation	109, 9, 10	⊢
	: , : , :
6	instantiation	44, 176	⊢
	: , : , : , : , : , : , :
7	generalization	11	⊢
8	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
9	instantiation	114, 12	⊢
	: , : , :
10	instantiation	109, 13, 14	⊢
	: , : , :
11	instantiation	15, 197, 183, 181, 16*	,  ⊢
	: , : , :
12	instantiation	109, 17, 18	⊢
	: , : , :
13	instantiation	134, 200, 195, 135, 19, 136, 57, 21	⊢
	: , : , : , : , : , :
14	instantiation	55, 135, 195, 200, 136, 20, 57, 21, 22*	⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.physics.quantum.QFT.invFT_on_matrix_elem
16	instantiation	23, 86, 87, 88	,  ⊢
	: , :
17	instantiation	114, 24	⊢
	: , : , :
18	instantiation	109, 25, 26	⊢
	: , : , :
19	instantiation	151	⊢
	: , :
20	instantiation	151	⊢
	: , :
21	modus ponens	27, 47	⊢
22	instantiation	28, 57, 176, 29*, 30*	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
24	modus ponens	31, 32	⊢
25	instantiation	114, 33	⊢
	: , : , :
26	instantiation	34, 35	⊢
	: , :
27	instantiation	36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
29	instantiation	143, 57	⊢
	:
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
31	instantiation	37, 176	⊢
	: , : , : , : , : , :
32	generalization	38	⊢
33	modus ponens	39, 40	⊢
34	theorem		⊢
	proveit.logic.equality.equals_reversal
35	instantiation	41, 136, 57	⊢
	: , :
36	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
37	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
38	instantiation	42, 43	⊢
	: , : , :
39	instantiation	44, 176	⊢
	: , : , : , : , : , : , :
40	generalization	45	⊢
41	modus ponens	46, 47	⊢
42	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
43	deduction	48	⊢
44	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
45	instantiation	109, 49, 50	,  ⊢
	: , : , :
46	instantiation	51, 200, 176, 135	⊢
	: , : , : , : , : , :
47	generalization	52	⊢
48	instantiation	134, 200, 195, 135, 53, 136, 58, 57, 59	,  ⊢
	: , : , : , : , : , :
49	instantiation	54, 135, 200, 136, 58, 57, 59	,  ⊢
	: , : , : , : , : , : , :
50	instantiation	55, 200, 195, 135, 56, 136, 57, 58, 59	,  ⊢
	: , : , : , : , : , :
51	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
52	instantiation	148, 58, 59	,  ⊢
	: , :
53	instantiation	151	⊢
	: , :
54	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
55	theorem		⊢
	proveit.numbers.multiplication.association
56	instantiation	151	⊢
	: , :
57	instantiation	85, 60, 61, 62	⊢
	: , :
58	instantiation	67, 64, 63	⊢
	: , :
59	instantiation	67, 64, 65	,  ⊢
	: , :
60	instantiation	198, 161, 66	⊢
	: , : , :
61	instantiation	67, 144, 68	⊢
	: , :
62	instantiation	69, 70, 71	⊢
	: , : , :
63	instantiation	120, 72, 73	⊢
	: , : , :
64	instantiation	198, 161, 74	⊢
	: , : , :
65	instantiation	75, 76	,  ⊢
	:
66	instantiation	198, 172, 77	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
68	instantiation	85, 117, 144, 92	⊢
	: , :
69	theorem		⊢
	proveit.logic.equality.sub_left_side_into
70	instantiation	78, 155, 79	⊢
	: , :
71	instantiation	114, 80	⊢
	: , : , :
72	instantiation	148, 123, 81	⊢
	: , :
73	instantiation	109, 82, 83	⊢
	: , : , :
74	instantiation	198, 164, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.negation.complex_closure
76	instantiation	85, 86, 87, 88	,  ⊢
	: , :
77	instantiation	198, 179, 194	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
79	instantiation	198, 89, 90	⊢
	: , : , :
80	instantiation	91, 117, 144, 92, 93*	⊢
	: , :
81	instantiation	120, 94, 95	⊢
	: , : , :
82	instantiation	134, 200, 124, 135, 96, 136, 123, 149, 119, 150	⊢
	: , : , : , : , : , :
83	instantiation	134, 135, 195, 124, 136, 125, 96, 144, 139, 149, 119, 150	⊢
	: , : , : , : , : , :
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
85	theorem		⊢
	proveit.numbers.division.div_complex_closure
86	instantiation	120, 97, 98	,  ⊢
	: , : , :
87	instantiation	198, 161, 99	⊢
	: , : , :
88	instantiation	103, 100	⊢
	:
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
90	instantiation	101, 160, 102	⊢
	: , :
91	theorem		⊢
	proveit.numbers.division.div_as_mult
92	instantiation	103, 178	⊢
	:
93	instantiation	109, 104, 105	⊢
	: , : , :
94	instantiation	148, 106, 150	⊢
	: , :
95	instantiation	134, 135, 195, 200, 136, 107, 149, 119, 150	⊢
	: , : , : , : , : , :
96	instantiation	140	⊢
	: , : , :
97	instantiation	148, 123, 108	,  ⊢
	: , :
98	instantiation	109, 110, 111	,  ⊢
	: , : , :
99	instantiation	198, 172, 112	⊢
	: , : , :
100	instantiation	113, 195, 192	⊢
	: , :
101	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
102	instantiation	198, 177, 197	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
104	instantiation	114, 115	⊢
	: , : , :
105	instantiation	116, 117, 118	⊢
	: , :
106	instantiation	148, 149, 119	⊢
	: , :
107	instantiation	151	⊢
	: , :
108	instantiation	120, 121, 122	,  ⊢
	: , : , :
109	axiom		⊢
	proveit.logic.equality.equals_transitivity
110	instantiation	134, 200, 124, 135, 126, 136, 123, 149, 150, 138	,  ⊢
	: , : , : , : , : , :
111	instantiation	134, 135, 195, 124, 136, 125, 126, 144, 139, 149, 150, 138	,  ⊢
	: , : , : , : , : , :
112	instantiation	198, 179, 188	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
114	axiom		⊢
	proveit.logic.equality.substitution
115	instantiation	127, 128, 176, 129*	⊢
	: , :
116	theorem		⊢
	proveit.numbers.multiplication.commutation
117	instantiation	198, 161, 130	⊢
	: , : , :
118	instantiation	198, 161, 131	⊢
	: , : , :
119	instantiation	198, 161, 132	⊢
	: , : , :
120	theorem		⊢
	proveit.logic.equality.sub_right_side_into
121	instantiation	148, 133, 138	,  ⊢
	: , :
122	instantiation	134, 135, 195, 200, 136, 137, 149, 150, 138	,  ⊢
	: , : , : , : , : , :
123	instantiation	148, 144, 139	⊢
	: , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
125	instantiation	151	⊢
	: , :
126	instantiation	140	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
128	instantiation	198, 141, 142	⊢
	: , : , :
129	instantiation	143, 144	⊢
	:
130	instantiation	145, 146, 197	⊢
	: , : , :
131	instantiation	198, 172, 147	⊢
	: , : , :
132	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
133	instantiation	148, 149, 150	⊢
	: , :
134	theorem		⊢
	proveit.numbers.multiplication.disassociation
135	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
136	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
137	instantiation	151	⊢
	: , :
138	instantiation	198, 161, 152	⊢
	: , : , :
139	instantiation	198, 161, 153	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
142	instantiation	198, 154, 155	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
144	instantiation	198, 161, 156	⊢
	: , : , :
145	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
146	instantiation	157, 158	⊢
	: , :
147	instantiation	198, 159, 160	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
149	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
150	instantiation	198, 161, 162	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
152	instantiation	198, 172, 163	⊢
	: , : , :
153	instantiation	198, 164, 165	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
155	instantiation	198, 166, 167	⊢
	: , : , :
156	instantiation	198, 172, 168	⊢
	: , : , :
157	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
159	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
160	instantiation	169, 170, 171	⊢
	: , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
162	instantiation	198, 172, 173	⊢
	: , : , :
163	instantiation	198, 179, 174	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
166	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
167	instantiation	198, 175, 178	⊢
	: , : , :
168	instantiation	198, 179, 191	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
170	instantiation	198, 177, 176	⊢
	: , : , :
171	instantiation	198, 177, 178	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
173	instantiation	198, 179, 180	⊢
	: , : , :
174	instantiation	198, 182, 181	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
176	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
177	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
178	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
179	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
180	instantiation	198, 182, 183	⊢
	: , : , :
181	assumption		⊢
182	instantiation	184, 185, 186	⊢
	: , :
183	assumption		⊢
184	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
185	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
186	instantiation	187, 188, 189	⊢
	: , :
187	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
188	instantiation	190, 191, 192	⊢
	: , :
189	instantiation	193, 194	⊢
	:
190	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
191	instantiation	198, 199, 195	⊢
	: , : , :
192	instantiation	198, 196, 197	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.negation.int_closure
194	instantiation	198, 199, 200	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
196	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
197	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
198	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
199	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements