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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	9, 5, 6*, 7*	⊢
	: , : , :
3	instantiation	16, 8	⊢
	: , :
4	instantiation	9, 10	⊢
	: , : , :
5	modus ponens	11, 12	⊢
6	instantiation	13, 108	⊢
	: , :
7	instantiation	13, 108	⊢
	: , :
8	modus ponens	14, 15	⊢
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	16, 17	⊢
	: , :
11	instantiation	18, 29	⊢
	: , : , : , : , : , : , :
12	generalization	19	⊢
13	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
14	instantiation	20, 29, 38, 26	⊢
	: , : , : , : , : , : , : , :
15	modus ponens	21, 22	⊢
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	modus ponens	23, 24	⊢
18	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
19	instantiation	25, 41, 26	,  ⊢
	: , :
20	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
21	instantiation	27, 29, 38	⊢
	: , : , : , : , : , :
22	generalization	33	⊢
23	instantiation	28, 125, 29, 84, 38, 85	⊢
	: , : , : , : , : , : , : , : , : , : , :
24	generalization	30	⊢
25	theorem		⊢
	proveit.numbers.multiplication.commutation
26	instantiation	53, 54, 31	⊢
	: , :
27	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
28	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
30	instantiation	32, 33, 34	,  ⊢
	: , : , :
31	instantiation	74, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.sub_left_side_into
33	instantiation	37, 38, 41, 39	,  ⊢
	: , : , : , :
34	instantiation	40, 41, 125, 84, 85, 48, 49, 51, 52	,  ⊢
	: , : , : , : , : , : , : , : , : , :
35	instantiation	91, 77, 42	⊢
	: , :
36	instantiation	70, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
38	instantiation	45, 59, 47, 48, 49	⊢
	: , : , :
39	instantiation	46, 59, 47, 48, 49, 50, 51, 52	,  ⊢
	: , : , : , :
40	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
41	instantiation	53, 54, 55	,  ⊢
	: , :
42	instantiation	74, 56, 57	⊢
	: , : , :
43	instantiation	83, 125, 78, 84, 58, 85, 77, 92, 93, 66	⊢
	: , : , : , : , : , :
44	instantiation	83, 84, 120, 78, 85, 79, 58, 88, 89, 92, 93, 66	⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
46	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
47	instantiation	94	⊢
	: , :
48	instantiation	60, 59	⊢
	:
49	instantiation	60, 61	⊢
	:
50	instantiation	94	⊢
	: , :
51	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
52	instantiation	62, 122, 108	,  ⊢
	: , :
53	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
54	instantiation	123, 98, 63	⊢
	: , : , :
55	instantiation	74, 64, 65	,  ⊢
	: , : , :
56	instantiation	91, 82, 66	⊢
	: , :
57	instantiation	83, 84, 120, 125, 85, 86, 92, 93, 66	⊢
	: , : , : , : , : , :
58	instantiation	90	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
61	instantiation	67, 120, 117	⊢
	: , :
62	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
63	instantiation	123, 103, 68	⊢
	: , : , :
64	instantiation	91, 77, 69	,  ⊢
	: , :
65	instantiation	70, 71, 72	,  ⊢
	: , : , :
66	instantiation	123, 98, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
69	instantiation	74, 75, 76	,  ⊢
	: , : , :
70	axiom		⊢
	proveit.logic.equality.equals_transitivity
71	instantiation	83, 125, 78, 84, 80, 85, 77, 92, 93, 87	,  ⊢
	: , : , : , : , : , :
72	instantiation	83, 84, 120, 78, 85, 79, 80, 88, 89, 92, 93, 87	,  ⊢
	: , : , : , : , : , :
73	instantiation	123, 101, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.equality.sub_right_side_into
75	instantiation	91, 82, 87	,  ⊢
	: , :
76	instantiation	83, 84, 120, 125, 85, 86, 92, 93, 87	,  ⊢
	: , : , : , : , : , :
77	instantiation	91, 88, 89	⊢
	: , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
79	instantiation	94	⊢
	: , :
80	instantiation	90	⊢
	: , : , :
81	instantiation	123, 106, 113	⊢
	: , : , :
82	instantiation	91, 92, 93	⊢
	: , :
83	theorem		⊢
	proveit.numbers.multiplication.disassociation
84	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
85	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
86	instantiation	94	⊢
	: , :
87	instantiation	123, 98, 95	,  ⊢
	: , : , :
88	instantiation	123, 98, 96	⊢
	: , : , :
89	instantiation	123, 98, 97	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
91	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
93	instantiation	123, 98, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
95	instantiation	123, 101, 100	,  ⊢
	: , : , :
96	instantiation	123, 101, 102	⊢
	: , : , :
97	instantiation	123, 103, 104	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
99	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
100	instantiation	123, 106, 105	,  ⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
102	instantiation	123, 106, 116	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
105	instantiation	123, 107, 108	,  ⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
107	instantiation	109, 110, 111	⊢
	: , :
108	assumption		⊢
109	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
110	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
111	instantiation	112, 113, 114	⊢
	: , :
112	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
113	instantiation	115, 116, 117	⊢
	: , :
114	instantiation	118, 119	⊢
	:
115	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
116	instantiation	123, 124, 120	⊢
	: , : , :
117	instantiation	123, 121, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.negation.int_closure
119	instantiation	123, 124, 125	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
121	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
122	assumption		⊢
123	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements