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	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
2	reference	16	⊢
3	reference	17	⊢
4	instantiation	15, 16, 17, 6	⊢
	: , : , :
5	modus ponens	7, 8	⊢
6	instantiation	9, 16, 17, 10, 11	⊢
	: , : , : , : , :
7	instantiation	12, 13, 22	⊢
	: , : , : , : , : , :
8	generalization	14	⊢
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
10	instantiation	15, 16, 17, 18	⊢
	: , : , :
11	instantiation	19, 37, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
14	instantiation	21, 22, 23, 24	⊢
	: , : , : , :
15	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
16	instantiation	25, 37	⊢
	:
17	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
18	instantiation	26, 95, 27	⊢
	: , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
20	instantiation	28, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
22	instantiation	31, 37	⊢
	:
23	instantiation	32, 33, 34	⊢
	: , :
24	instantiation	35, 95, 81	⊢
	: , :
25	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
26	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
27	assumption		⊢
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	36, 37	⊢
	:
30	instantiation	38, 95	⊢
	:
31	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
32	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
33	instantiation	96, 71, 39	⊢
	: , : , :
34	instantiation	48, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
36	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
37	instantiation	42, 93, 90	⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
39	instantiation	96, 76, 43	⊢
	: , : , :
40	instantiation	64, 51, 44	⊢
	: , :
41	instantiation	45, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
44	instantiation	48, 49, 50	⊢
	: , : , :
45	axiom		⊢
	proveit.logic.equality.equals_transitivity
46	instantiation	56, 98, 52, 57, 54, 58, 51, 65, 66, 60	⊢
	: , : , : , : , : , :
47	instantiation	56, 57, 93, 52, 58, 53, 54, 61, 62, 65, 66, 60	⊢
	: , : , : , : , : , :
48	theorem		⊢
	proveit.logic.equality.sub_right_side_into
49	instantiation	64, 55, 60	⊢
	: , :
50	instantiation	56, 57, 93, 98, 58, 59, 65, 66, 60	⊢
	: , : , : , : , : , :
51	instantiation	64, 61, 62	⊢
	: , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
53	instantiation	67	⊢
	: , :
54	instantiation	63	⊢
	: , : , :
55	instantiation	64, 65, 66	⊢
	: , :
56	theorem		⊢
	proveit.numbers.multiplication.disassociation
57	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
58	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
59	instantiation	67	⊢
	: , :
60	instantiation	96, 71, 68	⊢
	: , : , :
61	instantiation	96, 71, 69	⊢
	: , : , :
62	instantiation	96, 71, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
64	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
66	instantiation	96, 71, 72	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	instantiation	96, 74, 73	⊢
	: , : , :
69	instantiation	96, 74, 75	⊢
	: , : , :
70	instantiation	96, 76, 77	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
73	instantiation	96, 79, 78	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	96, 79, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
78	instantiation	96, 80, 81	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	instantiation	82, 83, 84	⊢
	: , :
81	assumption		⊢
82	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
83	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
84	instantiation	85, 86, 87	⊢
	: , :
85	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
86	instantiation	88, 89, 90	⊢
	: , :
87	instantiation	91, 92	⊢
	:
88	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
89	instantiation	96, 97, 93	⊢
	: , : , :
90	instantiation	96, 94, 95	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.negation.int_closure
92	instantiation	96, 97, 98	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
94	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
95	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
96	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat1