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, 7, 8, 9, 10, 11*	, , , , , , , , ,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_scalar_association
2	reference	13	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
4	instantiation	20	⊢
	: , : , : , :
5	reference	48	⊢
6	reference	49	⊢
7	reference	40	⊢
8	reference	41	⊢
9	reference	15	⊢
10	reference	16	, , , , ,  ⊢
11	instantiation	12, 13, 14, 15, 16	, , , , , , , , ,  ⊢
	: , : , :
12	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
14	instantiation	17, 18, 19	, , ,  ⊢
	: , : , :
15	instantiation	20	⊢
	: , : , : , :
16	instantiation	42, 21, 22	, , , , ,  ⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	47, 33, 23	, , ,  ⊢
	: , :
19	instantiation	24, 25, 26	, , ,  ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
21	instantiation	27, 28, 29	, , , , ,  ⊢
	: , :
22	instantiation	53, 30, 31	⊢
	: , : , :
23	instantiation	47, 40, 41	,  ⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	34, 32, 36, 35, 39, 37, 33, 40, 41	, , ,  ⊢
	: , : , : , : , : , :
26	instantiation	34, 35, 36, 37, 38, 39, 48, 49, 40, 41	, , ,  ⊢
	: , : , : , : , : , :
27	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
28	instantiation	42, 43, 44	, , , , ,  ⊢
	: , : , :
29	instantiation	45, 65, 66	,  ⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	instantiation	46	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	instantiation	47, 48, 49	,  ⊢
	: , :
34	theorem		⊢
	proveit.numbers.multiplication.disassociation
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	58	⊢
	: , :
39	instantiation	58	⊢
	: , :
40	assumption		⊢
41	assumption		⊢
42	theorem		⊢
	proveit.logic.equality.sub_left_side_into
43	instantiation	50, 60, 61, 51, 52	, , , , ,  ⊢
	: , : , : , :
44	instantiation	53, 54, 55	⊢
	: , : , :
45	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
47	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
48	assumption		⊢
49	assumption		⊢
50	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
51	instantiation	56, 60, 61, 57	, , , ,  ⊢
	: , : , :
52	assumption		⊢
53	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
55	instantiation	58	⊢
	: , :
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
57	instantiation	59, 60, 65, 61, 62, 63	, , , ,  ⊢
	: , : , : , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
60	instantiation	69, 77	⊢
	:
61	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
62	instantiation	64, 65, 66	,  ⊢
	: , :
63	instantiation	67, 76, 77, 68	, , ,  ⊢
	: , : , :
64	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
65	instantiation	69, 76	⊢
	:
66	assumption		⊢
67	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
68	modus ponens	70, 71	, , ,  ⊢
69	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
70	instantiation	72, 82, 73, 74	, ,  ⊢
	: , : , : , : , : , :
71	assumption		⊢
72	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
73	instantiation	75, 76, 77	,  ⊢
	: , :
74	instantiation	78, 79	⊢
	: , :
75	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
76	assumption		⊢
77	assumption		⊢
78	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
79	instantiation	80, 81, 82	⊢
	: , : , :
80	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
82	assumption		⊢
*equality replacement requirements