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, 6*	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
3	reference	9	⊢
4	instantiation	52	⊢
	: , : , :
5	instantiation	15, 7, 17	,  ⊢
	: , : , :
6	instantiation	8, 9, 10	,  ⊢
	: , :
7	instantiation	11, 54, 55, 22, 23	,  ⊢
	: , : , : , :
8	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
9	instantiation	12, 13, 14	⊢
	: , :
10	instantiation	15, 16, 17	,  ⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
12	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
13	instantiation	101, 72, 18	⊢
	: , : , :
14	instantiation	34, 19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.sub_left_side_into
16	instantiation	21, 54, 55, 22, 23	,  ⊢
	: , : , : , :
17	instantiation	24, 25, 26	⊢
	: , : , :
18	instantiation	101, 77, 27	⊢
	: , : , :
19	instantiation	59, 37, 28	⊢
	: , :
20	instantiation	29, 30, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
22	instantiation	53, 54, 55, 32	⊢
	: , : , :
23	instantiation	33, 100, 86	⊢
	: , :
24	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
26	instantiation	62	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
28	instantiation	34, 35, 36	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	45, 103, 38, 46, 40, 47, 37, 60, 61, 49	⊢
	: , : , : , : , : , :
31	instantiation	45, 46, 98, 38, 47, 39, 40, 50, 51, 60, 61, 49	⊢
	: , : , : , : , : , :
32	instantiation	41, 54, 55, 42, 43	⊢
	: , : , : , : , :
33	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	59, 44, 49	⊢
	: , :
36	instantiation	45, 46, 98, 103, 47, 48, 60, 61, 49	⊢
	: , : , : , : , : , :
37	instantiation	59, 50, 51	⊢
	: , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
39	instantiation	62	⊢
	: , :
40	instantiation	52	⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
42	instantiation	53, 54, 55, 56	⊢
	: , : , :
43	instantiation	57, 80, 58	⊢
	: , : , :
44	instantiation	59, 60, 61	⊢
	: , :
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	62	⊢
	: , :
49	instantiation	101, 72, 63	⊢
	: , : , :
50	instantiation	101, 72, 64	⊢
	: , : , :
51	instantiation	101, 72, 65	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
53	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
54	instantiation	66, 80	⊢
	:
55	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
56	instantiation	67, 100, 68	⊢
	: , :
57	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
58	instantiation	69, 70, 71	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
61	instantiation	101, 72, 73	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	instantiation	101, 75, 74	⊢
	: , : , :
64	instantiation	101, 75, 76	⊢
	: , : , :
65	instantiation	101, 77, 78	⊢
	: , : , :
66	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
67	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
68	assumption		⊢
69	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
70	instantiation	79, 80	⊢
	:
71	instantiation	81, 100	⊢
	:
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
74	instantiation	101, 83, 82	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	101, 83, 94	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
79	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
80	instantiation	84, 98, 95	⊢
	: , :
81	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
82	instantiation	101, 85, 86	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
85	instantiation	87, 88, 89	⊢
	: , :
86	assumption		⊢
87	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
88	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
89	instantiation	90, 91, 92	⊢
	: , :
90	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
91	instantiation	93, 94, 95	⊢
	: , :
92	instantiation	96, 97	⊢
	:
93	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
94	instantiation	101, 102, 98	⊢
	: , : , :
95	instantiation	101, 99, 100	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.negation.int_closure
97	instantiation	101, 102, 103	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
99	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
100	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
101	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
102	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
103	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements